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AGRICULTURAL   ARITHMETIC 


THE  MACMILLAN  COMPANY 

NEW  YORK   •    BOSTON    •    CHICAGO  •    DALLAS 
ATLANTA  •   SAN   FRANCISCO 

MACMILLAN  &  CO.,  Limited 

LONDON  •  BOMBAY  •  CALCUTTA 
MELBOURNE 

THE  MACMILLAN  CO.  OF  CANADA,  Ltd. 

TORONTO 


AGRICULTURAL  ARITHMETIC 


BY 


W.   T.   STRATTON,   A.M. 

ASSISTANT    PROFESSOR    OF    MATHEMATICS,    KANSAS    STATE 
AGRICULTURAL    COLLEGE 

AND 

B.   L.   REMICK,  Ph.M. 

PROFESSOR    OF    MATHEMATICS,    KANSAS    STATE 
AGRICULTURAL   COLLEGE 


Weto  gorfe 

THE   MACMILLAN   COMPANY 

1916 

All  rights  reserved 

3  7:rir'f 


COPTBIOHT,    1916, 

bt  the  macmillan  company. 


Set  up  and  electrotyped.     Published  June,  1916. 


Noiisaoti  $re08 

J.  8.  Gushing  Co.  —  Berwick  &  Smith  Co. 

Norwood,  Mass.,  U.S.A. 


QA 
\03 

PREFACE 

The  design  of  this  book  is  to  provide  a  brief 
course  in  arithmetic  for  students  interested  in  agri- 
culture. It  is  the  direct  outgrowth  of  a  need  for 
such  material  in  our  work  with  the  students  in  the 
School  of  Agriculture  of  the  Kansas  State  Agri- 
cultural College.  This  text  will  be  found  adapted 
to  the  requirements  of  advanced  classes  in  ele- 
mentary schools  in  communities  outside  the  city, 
the  agricultural  high  schools,  and  other  high  schools 
having  agricultural  courses.  It  presupposes  a  fair 
knowledge  of  the  principles  underlying  arithmetic 
and  some  facility  in  the  use  of  arithmetical  forms. 
Since  students  even  from  the  same  school  differ 
greatly  in  their  abilities  to  handle  readily  the  ordi- 
nary combinations  of  numbers,  it  has  been  found 
advisable  to  devote  some  time  to  a  review  of  the 
four  fundamental  operations,  common  fractions, 
and  decimals. 

The  purpose  throughout  the  book  has  been,  first 
of  all,  to  present  the  basic  principles  of  arithmetic. 
To  accomplish  this  end  use  is  made  of  the  prob- 
lems which  are  met  in  daily  experience.  Boys  and 
girls  of  any  community  can  master  the  principles 


vi  PREFACE 

of  arithmetic  to  the  best  advantage  when  those 
principles  are  applied  in  terms  of  their  own  en- 
vironment. Many  boys  and  girls  in  communities 
outside  of  large  cities  will,  moreover,  have  little  use 
for  purely  commercial  arithmetic,  and  if  they  do, 
they  will  come  to  it  better  from  the  training  they 
received  in  the  natural  way  with  real  problems  as 
they  know  them. 

The  agricultural  data  of  the  problems  are  based 
upon  the  most  recent  reports  of  the  various  State 
Experiment  Stations,  and  of  the  United  States  De- 
partment of  Agriculture.  From  the  facts  so  dis- 
played in  their  mathematical  relations  it  is  hoped 
that  the  students  may  not  only  obtain  sufficient 
material  for  drill  in  arithmetical  processes  but  also 
be  led  to  a  better  appreciation  of  farm  life. 

W.  T.  STRATTON. 
B.  L.  REMICK. 
April,  1916. 


ACKNOWLEDGMENTS 

The  authors  wish  to  acknowledge  their 
indebtedness  to  Miss  Daisy  Zeininger,  Mr. 
A.  R.  Fehn,  and  Miss  Ina  Holroyd  of  the 
department  of  mathematics  and  to  Mr. 
Hugh  Durham,  assistant  to  the  dean  of  ag- 
riculture, for  their  helpful  criticism  after 
having  used  the  material  in  pamphlet 
form  in  their  classes  at  the  Kansas  State 
Agricultural  College ;  also  to  Professor 
L.  E.  Call  of  the  department  of  agronomy 
and  Professor  H.  L.  Kent,  principal  of  the 
School  of  Agriculture  and  associate  pro- 
fessor of  education,  for  their  reading  of 
the  manuscript  from  an  agricultural  and 
from  an  educational  point  of  view. 

W.  T.  S. 
B.  L.  R. 


vli 


CONTENTS      . 

PAGE 

Addition 1 

Addition  of  United  States  Money 4 

Subtraction 7 

Subtraction  of  United  States  Money         ....  8 

Multiplication ■.        .10 

Multiplication  of  United  States  Money     ....  13 

Division 15 

Division  of  United  States  Money     .  .        .'       .        .19 

Common  Fractions 24 

Decimal  Fractions 36 

Farm  Accounts 55 

Denominate  Numbers 62 

Graphs  and  their  Applications 79 

Measurements 86 

Practical  Measurements 99 

Plastering,  Papering,  Painting,  Roofing,  Board  Measure, 
Flooring,  Cement  Construction,  Brickwork  and 
Stonework,  Temperature,  Longitude  and  Time, 
Standard  Time,  Government  Laud  Measure. 

Percentage 131 

Group  Problems  —  Seeds,  Dairying,  Poultry,  Fertilizers, 

Spraying,  Soils 141 

Gain  and  Loss  ■ .  154 

Commission 158 

Taxes 162 

Insurance        .        „     '  »        .        .        .        .        .        .        .  166 

Interest  .        .        .        , 170 

Ix 


X  CONTENTS 

PASS 

Business  Papers    ...,.,„..  180 

Powers  and  Roots 184 

Ratio  and  Proportion 192 

Practical  Applications  of  Ratio  —  Specific  Gravity,  Ra- 
tions, Nutritive  Ratio,  Balanced  Rations,  Silos         .  195 

Practical  Applications  of  Proportion  —  Levers         .        .  216 

Miscellaneous  Problems 219 

Appendix  I 235 

Weights  of  Produce,  Important  Facts,  Special   Rules, 
Hay  Measurements. 

Appendix  II 238 

Miscellaneous  Measures. 


AGRICULTURAL   ARITHMETIC 


FUNDAMENTAL  OPERATIONS 

ADDITION 
Study  Exercise 

1.  Addition  is  the  process  of  uniting  two  or  more 
numbers  into  one  number  called  the  sum. 

Speed  and  accuracy  in  addition  depend  largely 
upon  the  ability  to  combine  two  or  more  numbers 
into  one  number,  and  upon  constant  drill.  For 
several  days  a  few  minutes  of  each  recitation  period 
should  be  spent  in  drill  on  exercises  in  addition. 

Add  the  following  columns  : 


1. 

2. 

3. 

4. 

5. 

6. 

213 

8267 

549 

742 

785 

8645 

862 

1796 

753 

816 

905 

2619 

594 

9229 

927 

174 

783 

9641 

391 

7819 

289 

367 

427 

1862 

964 

8637 

918 

816 

716 

6529 

236 

908.8 

187 

952 

849 

5931 

567 

4245 

719 

657 

739 

1479 

198 

3278 

497 

185 

598 

5327 

671 

8931 

952 

189 

379 

7536 

278 

9677 

417 

579 

198 

2479 

2  FUNDAMENTAL  OPERATIONS 

Oral  and  Written  Exercise 

2.  Find  the  sum  first  without  rewriting,  and 
then  after  rewriting  the  columns. 

1.  176,  64,  368,  742,  984,  157,  18,  76,  591, 
723,  615,  458,  723,  659. 

2.  9341,  8967,  6259,  4637,  2687,  5412,  4219, 
6528,  6534,  7682,  1874.  . 

3.  873,  849,  196,  264,  973,  878,  585,  662,  791, 
653,  634,  972. 

4.  898,  626,  786,  741,  872,  677,  8^3,  997,  812, 
761,  876,  873. 

5.  569,  752,  625,  893,  369,  175,  461,  729,  527, 
538,  649,  129,  746. 

6.  731,  998,  431,  962,  877,  689,  398,  999,  689, 
476,  849,  327. 

7.  4894,  8796,  7842,  4988,  8921,  7639,  7289, 
7877,  7638,  4981,  3827,  4963. 

8.  829,  696,  628,  124,  297,  787,  382,  789,  271, 
197,  687,  397,  241,  473,  420. 

9.  The  circulation  of  a  daily  paper  was  34,699, 
34,464,  34,510,  34,541,  33,539,  34,618,  34,686, 
34,537,  34,588,  34,709,  34,681,  33,506,  34,715, 
34,564,  34,556,  34,579,  34,631,  34,599,  33,343, 
34,731,  34,534,  34,564,  34,658,  34,646,  34,606, 
34,600,  33,414,  34,568,  34,443,  34,498,  33,563. 
What  was  the  total  circulation  for  the  month  ? 


ADDITION  3 

Checking  Addition 

3.  In  addition  there  are  several  ways  of  check- 
ing the  result,  but  only  two  are  worthy  of  con- 
.sideration  here. 

Adding  the  columns  up  and  then  doum.  Add  the 
columns,  beginning  at  the  top.  Then  add  them 
again,  beginning  at  the  bottom.  If  the  sums  are 
found  to  be  the  same,  the  result  is  probably  correct. 
The  check  comes  from  the  fact  that  different  com- 
binations of  figures  are  used  in  each  addition,  and 
thus  the  danger  of  making  the  same  mistake  over 
and  over  again  is  eliminated. 

Casting  out  the  nines.  To  check  by  casting  out 
the  nines,  first  add  the  digits,  and,  when  the  sum 
equals  or  exceeds  nine,  drop  the  nine.  Do  the  same 
for  the  result  and  the  remainders  obtained.  If  the 
final  remainder  equals  the  remainder  of  the  sum, 
the  result  is  probably  correct.     For  example : 

463  4,  remainder 

327  3,  remainder 

784  1,  remainder 

914  5,  remainder 

748  1,  remainder 

318  3,  remainder 

536  5,  remainder 

679  4,  remainder 

4769  8,  remainder 

8  is  the  final  remainder 


4  FUNDAMENTAL  OPERATIONS 

Checking  Exercise 

4.  Find  the  total  number  of  horses,  mules,  milch 
cows,  sheep,  hogs,  and  beef  cattle  found  in  the 
ten  leading  live  stock  states.  Also  from  the  table 
find  the  total  number  of  animals  in  each  of  the 
states  given.  Check  by  the  two  methods  suggested 
above. 


State 

Horses 

Mu  LES 

Milch 
Cows 

Sheep 

Hogs 

Beef 

Cattle 

Illinois 

1497 

151 

1049 

1068 

4640 

1266 

Kansas 

1169 

218 

698 

326 

2808 

1872 

Indiana 

838 

84 

634 

1372 

4031 

1266 

Iowa 

1568 

57 

1394 

1201 

9689 

2773 

Missouri 

1095 

333 

822 

1755 

4491 

1504 

Wisconsin 

652 

3 

1504 

874 

2051 

1146 

Ohio 

901 

24 

887 

3694 

3578 

855 

Texas 

1158 

703 

1034 

2032 

2544 

5177 

Nebraska 

1059 

85 

613 

382 

1104 

2002 

New  York 

609 

4 

1495 

911 

777 

894 

Note.  —  The  numbers  above  are  thousands  —  the  three  ciphers 
are  omitted. 


ADDITION   OF  UNITED   STATES  MONEY 

5.  In  addition  of  United  States  money  the  num- 
bers to  be  added  should  be  so  placed  that  the  deci- 
mal points  shall  stand  in  a  vertical  line.  Add  as 
in  whole  numbers.  The  decimal  point  in  the  sum 
should  stand  directly  under  the  decimal  points  of 
the  numbers  to  be  added. 


ADDITION  5 

Written  Exercise 
6.    Find  the  sum  of  the  following : 

1.  $8.65,  $9.56,  $16.76,  $18.24,  $17.73, 
$93.50,    $1.97,    $9.32,    $6.84. 

2.  $93.20,  $77.42,  $65.94,  $43.59,  $182.47, 
$65.79,  $176.44,  $89.57. 

3.  $118.46,  $92.75,  $169.84,  $145.38,  $71.62, 
$233.90. 

4.  $362.45,  $277.53,  $916.37,  $49.12,  $635.26, 
$528.05. 

5.  $806.72,  $1215.64,  $2390.29,  $1914.40, 
$1750.75. 

6.  $9803.14,    $736.45,   $10,041.82,    $1667.15, 

$5981.38. 

Written  Problems 

7.  1.  A  farmer  sold  the  following  products  dur- 
ing the  year:  3  horses  at  $255  each;  24  hogs  for 
$478.60;  14  steers  for  $692.75;  360  bushels  of 
potatoes  for  $213.22;  40  chickens  for  $24.80; 
110  dozen  eggs  for  $23.10;  and  550  bushels  of 
oats  for  $220.     Find  the  total  amount  of  the  sales. 

2.  The  estimated  cost  of  raising  an  acre  of 
wheat  is  as  follows:  plowing,  $1.38;  preparing 
land,  $1.06;  seed,  $1.12;  drilling,  $.40;  cutting, 
$1.00;  threshing,  $.80;  labor  in  threshing,  $.83 ; 
hauling  to  market,  $.43;  rent  on  land,  $2.40; 
taxes,  $.25.  What  is  the  estimated  cost  of  raising 
an  acre  of  wheat  ? 


6  FUNDAMENTAL  OPERATIONS 

3.  The  estimated  cost  of  raising  an  acre  of  corn 
is  as  follows:  seed,  $.13  ;  plowing,  $1.31;  preparing 
land,  $.54;  planting,  $.24;  cultivating,  $1.81; 
husking,  $3.46;  rent  and  taxes,  $2.90.  What  is 
the  estimated  cost  of  raising  an  acre  of  corn  ? 

4.  What  was  the  entire  cost  of  a  silo  if  the 
foundation  cost  $17.53;  lumber,  $5;  staves, 
$28.84;  hauling,  $9;  hoops,  $21.95;  nails  and 
bolts,  $5.70;  labor,  $17.50;  painting,  $12.50; 
incidental  expenses,  $9.50  ? 

5.  The  actual  cost  of  one  of  the  silos  built  at  the 
Iowa  Station  was  distributed  as  follows :  excava- 
tion, $5.65 ;  foundation,  $35.10  ;  hoops  and  braces, 
$46.50;  inside  walls,  $65;  outside  walls,  $37.50; 
roof,  $11.62;  chute,  $16.30;  hardware,  $12.15; 
labor,  $25.     What  was  the  entire  cost  of  the  silo  ? 

6.  The  amount  of  money  in  circulation  in  the 
United  States  during  1915  was  distributed  as  here 
given :  gold  coin,  $657,944,193 ;  gold  certificates, 
$931,390,259;  silver  dollars,  $70,724,311;  silver 
certificates,  $482,892,121;  other  silver,  $161,565,- 
114;  treasury  notes,  $2,388,789;  United  States 
Bank  notes,  $336,974,240;  national  bank  notes, 
$1,050,869,169.  What  was  the  total  amount  of 
money  in  circulation  ? 


SUBTRACTION 
Study  Exercise 

8.  Subtraction  is  the  process  of  finding  the  dif- 
ference between  two  numbers. 

The  number  from  which  we  subtract  is  called  the 
minuend. 

The  number  to  be  subtracted  is  called  the  sub- 
trahend. 

The  remainder,  or  difference,  is  the  result  ob- 
tained by  subtraction. 

Subtract : 

1.  2.  3.  4.  5.  6.  7. 

8423  7549  6371  9420  7421  5487  8412 
2089  3507  1729  2679  3268  4218  4189 


Oral  Exercise 

9.    Give  the  answer : 

1.   7836-429  = 

7. 

1003-548  = 

2.     763-   89  = 

8. 

872-428  = 

3.     645-247  = 

9. 

1043-769  = 

4.     963-689  = 

10. 

4321-978=  . 

5.     689-437  = 

11. 

1007-967  = 

6.     823-479  = 

12. 

451-265  = 

8  FUNDAMENTAL  OPERATIONS 

13.  1024-198=  16.    1256-958  = 

14.  686-298=  17.   2150-359  = 

15.  750  -  543  =  18.    1025  -  493  = 

Checking  Subtraction 

10.  To  check  a  problem  in  subtraction,  find  the 
sum  of  the  subtrahend  and  the  remainder.  If 
their  sum  equals  the  minuend,  the  work  is  probably 
correct. 

For  example  :  From  5763  take  3872. 

Process 

Explanation :    Without  rewriting,  add   the 

numbers  in  the  subtrahend  and  remainder,  and 
S872 
check  with  the  minuend. 

1891  Ans. 
Subtract  and  check  the  following : 

1.  2.  3.  4.  5.  6. 

9873  96763  68347  78865  92476  78421 
4584  78974  57638  34968  64384  58465 

SUBTRACTION   OF  UNITED   STATES  MONEY 

11.  In  subtraction  of  United  States  money  the 
numbers  to  be  subtracted  should  be  so  placed  that 
the  decimal  points  stand  in  a  vertical  line.  Sub- 
tract as  in  whole  numbers.  The  decimal  point  in 
the  remainder  should  stand  directly  under  the 
decimal  points  of  the  numbers  to  be  subtracted. 

1.  From  $197.17  take  $89.97;  from  $76.43 
take  $43,465. 


SUBTRACTION  9 

2.  From  $  530.38  take  $416.71;  from  $325.62 
take  $  219.74. 

3.  From  $  604.19  take  $511.28;  from  $498.16 
take  $269.77. 

4.  From  $368  take  $314.06;  from  $805.10 
take  $  732.49. 

Written  Problems 

12.  1.  A  man  deposited  in  a  bank  $970.35.  He 
checked  out  at  one  time  $269.75,  at  another 
$180.13,  at  another  $347.86,  and  at  another 
$45.80.     How  much  remained  ? 

2.  A  school  district  has  a  levy  of  $750  for 
school  purposes.  What  is  left  on  hand  at  the  end 
of  the  year  if  the  following  amounts  were  paid : 
teacher's  salary,  $480;  fuel,  $47.50;  repairs, 
$35.75;  equipment,  $40;   incidentals,  $37.50  ? 

3.  What  will  be  the  change  if  a  $10  bill  is 
presented  in  payment  for  each  of  the  following 
bills:  $6.33;  $8.23;  $5.95;  $4.72;  $3.45;  $.76; 
$8.15;  $2.10? 

4.  What  will  be  the  change  if  a  $20  bill  is 
presented  in  payment  for  each  of  the  following 
bills:  $17.32;  $9.76;  $18.21;  $14.87;  $9.62; 
$12.55;  $6.18;  $7.96? 

5.  A  carload  of  cattle  sold  for  $3457.40.  What 
was  left  after  paying  the  following  expenses  :  com- 
mission, $15.60;  freight,  $21;  yardage,  $4.70; 
feed  on  the  road,  $2.85  ? 


MULTIPLICATION 
Study  Exercise 

13.  Multiplication  is  the  process  of  repeating  a 
number  a  certain  number  of  times. 

The  number  to  be  repeated  is  called  the  multi- 
plicand. 

The  number  showing  the  number  of  times  the  mul- 
tiplicand is  to  be  repeated,  is  called  the  multiplier. 

The  result   obtained   by  performing  the  multi- 
plication is  called  the  product. 
.  The  multiplicand  may  be  either  an  abstract  or 
a  concrete  number,  but  the  multiplier  is  always 
abstract. 

Since  speed  and  accuracy  can  only  be  attained 
by  drill,  the  student  should  practice  on  problems 
in  multiplication  until  he  is  entirely  familiar  with 
the  process,  and  especially  with  the  short  rules  of 
multiplication. 

Written  Exercise 

14.  Multiply: 

1.  2.  3.  4.  5. 

397    383    864    5963    4246 
68     37     59    478    629 


6. 

7. 

8. 

9. 

10. 

7269 

8327 

9873 

8967 

9003 

943 

684 

763 

479 

7008 

10 


MULTIPLICATION  11 

SHORT   METHODS   IN   MULTIPLICATION 

15,  The  most  important  short  methods  of  multi- 
plication are  the  following : 

1.  To  multiply  hy  10,  100,  1000,  etc.,  annex 
one,  two,  three,  etc.,  ciphers  to  the  multiplicand. 

2.  To  multiply  hy  the  factors  of  a  nuTnber  rather 
than  to  multiply  by  the  number  itself.  For  ex- 
ample, to  multiply  by  18,  first  multiply  by  6  and 
then  by  3.  The  result  is  thus  obtained  without 
addition,  and  the  multiplication  has  been  performed 
without  rewriting. 

3.  To  multiply  hy  19,  29,  39,  etc.,  multiply  by  the 
next  higher  number  and  subtract  the  number  from 
the  result.  For  example,  to  multiply  by  99,  first 
multiply  by  100,  i.e.  annex  two  ciphers,  and  then 
subtract  the  number. 

Apply  short  methods  in  the  following  exercises : 

1.  Multiply  247  by  100. 

247  X  100  =  24700  (annex  two  ciphers). 

2.  Multiply  376  by  28. 

376  X  28  =  376  X  4  X  7  =  1504  x  7  =10528. 

3.  Multiply  367  by  29. 

29  X  367  =  3(10  X  367)  -  367  =  11010  -  367  =  10643. 

Written  Exercise 

16.  Perform  the  following  multiplications,  using 
as  far  as  possible  the  short  methods  of  multi- 
plication. 


12  FUNDAMENTAL  OPERATIONS 

1.  Multiply  9247  by  10,  100,  1000,  10000. 

2.  Multiply  7483  by  9,  19,  29,  39,  49,  59,  69, 
79,  89,  99. 

3.  Multiply  6384  by  18,  24,  28,  36,  42,  56,  using 
the  factors. 

4.  Multiply  768  by  47 ;  8549  by  87 ;  4581  by 
23  ;  7538  by  269. 

5.  Multiply  1001  by  287  ;  56843  by  98  ;  29378 
by  89  ;  78635  by  457. 

6.  Multiply  96  by  78  by  37 ;  45  by  28  by  79 ; 
65  by  73  by  87. 

7.  Multiply  65,942  by  758;  78,658  by  4937; 
6389  by  574. 

8.  Multiply  3258  by  64  by  94 ;  468  by  8276. 

Written  Problems 

17.  1.  One  cubic  foot  of  soil  weighs  about  79 
pounds.  The  soil  8  inches  deep  on  an  acre  con- 
tains 29,040  cubic  feet.     What  islts  weight  ? 

2.  Multiply  the  sum  of  746  and  388  by  three 
times  their  difference. 

3.  If  a  cow  averages  29  pounds  of  milk  a  day, 
how  many  pounds  does  she  produce  in  a  year  ? 

4.  Sound  travels  1130  feet  a  second.  How  far 
will  it  travel  in  43  seconds  ? 

5.  A  wheat  field  of  17  acres  yields  26  bushels 
an  acre.     How  many  bushels  are  produced  ? 


MULTIPLICATION  13 

6.  If  a  dairy  cow  eats  38  pounds  of  silage  a  day, 
how  many  pounds  of  silage  will  it  take  to  feed  a 
herd  of  24  cows  for  160  days  ? 

Checking  Multiplication 

18.  The  best  method  of  checking  the  result  in 
multiplication  is  to  interchange  the  multiplier  and 
multiplicand.  Thus,  to  check  the  product  of  894 
by  635,  multiply  635  by  894.  If  the  same  prod- 
uct is  obtained  in  each  case,  the  result  is  probably 
correct. 

Multiply  and  check  : 

4.  5.  6.  7. 

2367     7429     4198     82,479 
2581     _689     _679 19 

MULTIPLICATION    OF    UNITED    STATES   MONEY 

19.  In  multiplication  of  United  States  money 
multiply  as  in  whole  numbers,  and  point  off  the 
dollars  from  the  cents  and  mills. 

Multiply  : 


1. 

2. 

3. 

6743 

7356 

2845 

574 

549 

7031 

1. 

$46.75 
18 

2. 

$64.58 
36 

3. 

$86.41 
96 

4. 

$56.46 

78 

5. 

$89.63 
69 

6. 

$472.35 
64 

7. 

$100.35 
403 

8. 

$964.83 
38 

14  FUNDAMENTAL  OPERATIONS 

Written  Problems 

20.  1.  If  the  cost  of  raising  a  crop  of  wheat  is 
$9.67  an  acre,  what  is  the  total  cost  to  raise  65 
acres  ? 

2.  Corn  can  be  produced  for  about  $  10.06  an 
acre.     What  will  be  the  cost  to  raise  65  acres  ? 

3.  If  the  wheat  in  problem  1  averaged  18 
bushels  an  acre  and  is  valued  at  95 1^  a  bushel, 
what  was  the  profit  ? 

4.  If  the  corn  averaged  35  bushels  an  acre  and 
was  valued  at  65  ^,  what  was  the  profit  ?  Compare 
with  the  result  of  problem  3. 

5.  What  is  the  value  of  a  carload  of  58  hogs 
averaging  316  pounds  at  8  ^  a  pound  ? 

6.  The  United  States  imported  38  million 
bunches  of  bananas  during  a  certain  year.  Find 
their  cost  at  an  average  value  of  24 <^  a  bunch. 

7.  What  will  be  the  cost  of  a  fertilizer  for  4.5 
acres  of  potatoes  at  $3.75  per  acre? 

8.  If  in  spraying  an  apple  tree  four  times  with 
Bordeaux  mixture  the  cost  is  12  (^  for  the  material 
and  23^  for  labor,  what  will  it  cost  to  spray  85 
trees  four  times  ? 

9.  What  will  be  the  cost  of  spraying  the  trees 
in  problem  8  if  a  lime-sulphur  treatment  is  used 
with  an  average  cost  of  17)^  per  tree  for  the  mate- 
rial and  with  the  labor  cost  the  same  ? 


DIVISION 
Study  Exercise 

21.  Division  is  the  process  of  separating  a  num- 
ber into  equal  parts. 

The  number  to  be  separated  is  called  the  dividend. 

The  number  that  shows  into  how  many  parts 
the  dividend  is  to  be  separated  is  called  the  divisor. 

The  result  obtained  by  division  is   called   the 

quotient. 

Short  Division 

Divide  6879  by  3. 

Process  Explanation :  6  thousands  divided  by  3 

Qsggjg  equals  2  thousands ;   8  hundreds  divided 

2293    4„o       t)y  3  equals  2  hundreds,  with  a  remainder 

of  2  hundreds ;    2  hundreds  plus  7  tens 

equals  27  tens ;  27  tens  divided  by  3  equals  9  tens  ;  9  units 

divided  by  3  equals  3  units.     Therefore  the  quotient  is  2293. 

Long  Division 

Process  Explanation:  576  thousands  di- 

1356^11  Ans.      vided  by  425  equals  1  thousand, 

425)576408  with  a  remainder  of  151  thousands ; 

425  151   thousands    plus   4  hundreds 

1514  equals  1514  hundreds  ;  1514  hun- 

1275  dreds  divided  by  425  equals  3  hun- 

2390  dreds,  with  a  remainder  of  239 

2125  hundreds ;    239  hundreds  plus  0 

2658  tens  equals  2390  tens ;  2390  tens 

2550  divided  by  425  equals  5  tens,  with 

108  a  remainder  of  265  tens  ;  265  tens 

plus  8  units  equals  2658  units ;  2658  units  divided  by  425 

16 


16  FUNDAMENTAL  OPERATIONS 

equals  6  units,  with  a  remainder  of  108  units.     Therefore 
the  quotient  is  1356  with  a  remainder  of  108  or  13o6^||. 

Oral  Exercise 

22.  Divide  in  short  division : 

1.  Divide  68,  642,  568,  4628,  468,  864,  972, 
794,  9755,  371,  279  by  2,  3,  and  4. 

2.  Divide  144,  657,  489,  843,  198,  1758,  4275, 
63,285,  8537,  4631  by  3  and  5. 

3.  Divide  288,  1456,  5348,  5228,  5608,  9417, 
57,436,  18,764  by  4  and  6. 

4.  Divide  359, 1375,  20,849,  3148,  50,842,  3749, 
2748,  5648,  3298,  9076  by  7. 

5.  Divide   6785,   4873,   9864,   76,548,   35,638, 
53,789,  10,856,  190,834  by  8  and  9. 

Written  Exercise 

23.  Divide  in  long  division  : 

1.  Divide  378  by  14  ;  1411  by  17  ;  1728  by  12  ; 
2401  by  49. 

2.  Divide  5208  by  56;    5060  by  46;    9417  by 
73;  21,465  by  81. 

3.  Divide  10,252  by  97 ;  8795  by  103  ;  13,651 
by  89;  19,407  by  113. 

4.  Divide    19,404    by   231;    28,763    by   314; 
49,706  by  467. 

5.  Divide  690,014   by  523;    803,277    by  633; 
746,292  by  809. 


DIVISION  17 

Tests  of  Divisibility 

24.  In  order  to  determine  what  factors  will 
exactly  divide  a  number,  the  following  tests  of  di^ 
visibility  of  numbers  are  suggested : 

A  number  is  divisible  by  2  if  it  ends  in  an 
even  number,  by  3  if  the  sum  of  the  digits  is 
divisible  by  3,  by  4  if  the  number  formed  by  tbe 
last  two  digits  of  the  number  is  divisible  by  4,  by 
5  if  the  number  ends  in  5  or  zero,  by  6  if  divisible 
by  2  and  3,  by  8  if  the  number  formed  by  the  last 
three  digits  is  divisible  by  8,  by  9  if  the  sum  of  the 
digits  is  divisible  by  3  twice,  and  by  10  if  the 
number  ends  in  zero. 

Test  the  divisibility  of  the  following  numbers  and 
tell  what  integers  will  exactly  divide  each  number. 

1.  386    3.     720    5.  6375    7.     6789      9.      1548 

2.  159    4.  2912    6.   7930    s.  40752    lo.  31,581 

Checking  Division 

25.  To  check  the  work  in  division,  multiply  the 
quotient  by  the  divisor  and  to  this  product  add  the 
remainder,  if  any. 

Divide  and  check  the  following : 

1.  179^5.  6.      52,968-^236. 

2.  6184^4.  7.        7162^24. 

3.  37,121-^163.  8.   216,509-^127. 

4.  367-13.  9.        9086^11. 

5.  45,075^15.  10.    754,190^105. 


18  FUNDAMENTAL  OPERATIONS 

Short  Methods  m  Division 

26.  The  most  important  short  methods  in 
division  are  the  following  : 

To  divide  by  10,  100,  1000,  etc.,  set  off  as  many 
figures  at  the  right  of  the  dividend  as  there  are 
ciphers  in  the  divisor.  The  figures  thus  set  off  are  the 
remainder,  and  the  other  figures  are  the  quotient. 

Division  may  often  be  performed  more  easily  by 
usiiig  the  factors  of  the  number  as  divisors.  For 
example,  to  divide  by  18,  first  divide  by  3  and  then 
by  6. 

Apply  short  methods  in  the  following  exercises : 

1.  Divide  42,713  by  100. 

Process 

427|13  =  427^1^. 

2.  Divide  3405  by  15. 

Process 
5 1 3405 
3 1 681 
227  Arts. 

Written  Exercise 

27.  Use  short  methods. 

1.  Divide  5268  by  12,  100,  1000. 

2.  Divide  8498  by  10,  14,  21. 

3.  Divide  23,040  by  16,  72,  96. 

4.  Divide  7560  by  35,  60,  45. 

5.  Divide  17,010  by  90,  42,  54. 


DIVISION  19 

DIVISION    OF   UNITED    STATES    MONEY 

28.  To  divide  in  United  States  money,  proceed 
as  in  whole  numbers.  Write  the  first  figure  of  the 
quotient  over  the  right-hand  figure  of  the  first 
partial  dividend.  Place  the  decimal  point  in  the 
result,  directly  over  the  decimal  point  in  the 
dividend. 

In  case  both  dividend  and  divisor  represent 
amounts  of  money,  reduce  them  to  cents  and  then 
divide  as  usual. 

1.    Divide  $  528.08  by  92. 

Process 

$5.74   Ans. 


92)528.08 
460 
680 
644 
368 
368 


Written  Exercise 
29.   Find  the  quotient. 

1.  $22.68 -f- 14.  6.  $985.09^23. 

2.  $22.68^114.  7.  $1662.60^51. 

3.  $65.25-^18.  8.  $1791.70^46. 
:^   4.    $1166.20^28.      .  9.  $2734.40^64. 

I    5.       $74.50  H- $.25.  10.  $443.20^  $32. 


20  FUNDAMENTAL  OPERATIONS 

Written  Problems 

30.  1.  A  farmer  paid  $64,650  for  862  acres  of 
land.     What  was  the  price  per  acre  ? 

2.  If  $250,  invested  at  Q^%  simple  interest, 
yield  $16.25  a  year,  how  many  years  will  be  re- 
quired for  it  to  double  itself  ? 

3.  How  many  pounds  of  sugar  at  6l^  a  pound 
can  be  had  in  exchange  for  17  dozen  eggs  at  24^  a 
dozen  ? 

4.  The  approximate  value  of  the  corn  crop  of 
Morgan  County,  Illinois,  in  1910  was  $2,950,000, 
and  the  crop  acreage  128,348.  Find  the  value  of 
the  yield  per  acre. 

5.  The  area  of  the  farm  lands  of  Iowa  in  1910  was 
about  34  million  acres,  and  their  value  3260  million 
dollars.     What  was  their  average  value  per  acre  ? 

6.  According  to  recent  statistics  the  annusil 
wages  paid  to  the  222,264  iron  and  steel  workers 
in  the  United  States  during  a  certain  year  was 
$120,723,092.  What  was  the  average  wage  of 
each  earner  ? 

REVIEW   OF   FUNDAMENTAL   OPERATIONS 
Written  Exercise 

31.  Perform  the  operations  indicated. 

1.  8462  +  5179-6384-2176  =  ? 

2.  486-317  +  479  +  821-782-238  =  ? 


DIVISION  21 

3.  6917-418-1670  +  592  =  ? 

4.  783x985^428  =  ? 

5.  745x348^87=? 

6.  5275.50-4-5.66  +  247-499  =  ? 

7.  403-^13  +  46x15-124  =  ? 

(Perform  all  multiplication  and  division  before 
adding  and  subtracting.) 

8.  4914^7-652x19  +  234  =  ? 

9.  89x74x153^91  =  ? 

10.  Select  the  numbers  from  the  following  that 
are  exactly  divisible  bv  2,  3,  4,  5,  6,  7,  8,  9  :  376, 
653,  981,  4328,  35,4^^56,  92,125,  82,601,  9212, 
3730,  3645,  42,563,  67,332,  85,563,  9656,  9985, 
2708,  61,083,  98,254,  89,576. 

Written  Problems 

32.  1.  A  horse  is  fed  16  pounds  of  hay  per  day. 
How  many  tons  will  be  required  to  keep  the  horse 
a  year  ? 

2.  In  five  bins  of  wheat  there  are  567  bushels, 
237  bushels,  478  bushels,  654  bushels,  and  825 
bushels.     How  many  bushels  in  the  five  bins  ? 

3.  At  Columbia,  Mo.,  the  total  wind  movement, 
according  to  the  U.  S.  weather  report,  for  July  was 
4637  miles,  for  August  4378  miles,  for  September 
4869  miles.  What  was  the  total  wind  movement 
for  the  three  months  ?     What   was   the   average 


22  FUNDAMENTAL  OPERATIONS 

wind  movement  per  day  for  each  month  ?  For 
the  entire  ,  time  ?  What  was  the  average  wind 
movement  per  hour  for  the  different  months  ?  For 
the  entire  time  ? 
/  4.  The  Santa  Fe  trail  is  about  775  miles  in 
•  length ;  the  Oregon  trail  is  1048  miles.  How  much 
longer  is  the  Oregon  trail  than  the  Santa  Fe  trail  ? 

5.  What  is  the  total  weight  of  a  carload  of  24 
steers,  if  they  average  1296  pounds  ? 

6.  At  a  waterworks  station  two  large  pumps 
/and   four  small  ones  were  pumping.     The  large 

"^  pumps  delivered  1600  gallons  each  per  minute,  and 
the  small  ones  400  gallons  each  per  minute.  How 
many  gallons  were  pumped  per  hour  ? 

7.  A  man  earns  $75  per  month  and  his  ex- 
penses average  $57  per  month.  How  much  will 
he  save  per  year  ? 

8.  In    order  to   produce  a  ton  of  clover   hay, 
•^about    375    tons    of   water    are   necessary.     How 

many  tons  will  be  used  in  producing  27  tons  of 
clover  hay  ? 

9.  A  wagon  weighs  1700  pounds.  The  wagon 
loaded  Avith  coal  weighs  1800  pounds  more  than 
twice  as  much  as  the  wagon.  What  was  the 
weight  of  the  coal  ? 

10.  It  takes  16  hours  to  coal  a  battleship.  How 
many  tons  will  it  hold  if  it  is  loaded  at  the  rate  of 
163  tons  per  hour  ? 


DIVISION  23 

11.  If  it  costs  $1.90  per  ton  to  mine  soft  coal 
and  ship  it  to  market,  what  will  a  carload  of  43 
tons  cost,  allowing  a  profit  of  42  cents  per  ton  to 
the  mine  owner  ? 

12.  If  the  coal  is  sold  at  retail  at  $5  per  ton, 
what  is  the  profit  to  the  dealer  for  handling  the 
coal  in  problem  11  ? 

13.  If  a  farmer  sold  a  quantity  of  wheat  for 
$988.20,  how  many  bushels  did  he  sell  if  he  re- 
ceived 90  cents  per  bushel? 

14.  If  hogs  are  selling  at  $7.45  per  cwt.,  what  is 
a  300-pound  hog  worth  ?  How  much  will  a  load  of 
hogs  bring  if  the  total  weight  of  the  hogs  and  wagon 
is  4297  pounds  and  the  wagon  weighs  1541  pounds  ? 

15.  If  there  are  12  hogs  in  the  load,  what  is 
their  average  weight  ?     Their  average  selling  price  ? 

16.  During  1913,  1,197,892  foreign  immigrants 
came  to  the  United  States.  What  was  the  average 
number  per  month  ?     Per  day  ? 

17.  In    Allen    county,    Kansas,    896    acres    of 
potatoes  in  1910  produced  68,888  bushels,  valued  ^y 
at   $55,910.40.     What  was  the  average  yield  per 
acre  ?     The  average  value  ? 

18.  How  many  pounds  are  there  in  a  bushel  of 
shelled  corn  if  32  bushels  weigh  1792  pounds  ? 

19.  A  balloon  will  lift  a  weight  of  1000  pounds. 
How  many  men,  averaging  160  pounds,  will  be 
required  to  hold  the  balloon  down  ? 


COMMON  FRACTIONS 

Study  Exercise 

33.  A  fraction  is  an  indicated  division. 

The  dividend,  or  the  number  above  the  line,  is 
called  the  numerator ;  the  divisor,  or  the  number 
below  the  line,  is  called  the  denominator. 

The  numerator  and  the  denominator  are  called 
the  terms  of  a  fraction. 

If  a  fraction  is  less  than  unity,  it  is  called  a 
proper  fraction ;  if  it  is  equal  to  or  greater  than 
unity,  it  is  called  an  improper  fraction. 

The  form  of  a  fraction  may  be  changed  without 
altering  its  value  by  reducing  the  fraction  to 
higher  terms  or  lower  terms. 

REDUCING   TO   LOWER  TERMS 

34.  To  reduce  a  fraction  to  its  lowest  terms 
divide  the  numerator  and  denominator  by  the 
same  number ;  continue  to  divide  by  common 
factors  until  both  terms  are  prime. 

1.    Reduce  ||^|  to  lowest  terms. 

Process 

222^111 

246     123' 

111     37       . 

=  — -  •    Ans. 

123      41 

24 


COMMON  FRACTIONS  25 

Oral  and  Written  Exercise 

2.  Reduce  3-%  ;  f  J ;  yf  5  3  f  5  if  *^  their  lowest 
terms. 

J.     x\euuctJ     gy,     124'     135'     255'     864      ^"     L-UtiJI 

lowest  terms. 

4.  Reduce  |f ;  ^^--^ ;  f  f ;  jl/^  to  lowest 
terms. 

5.  Reduce  If  J;  iff;  iff;  2V1  to  lowest  terms. 

CHANGING   TO   HIGHER  TERMS 

35.  To  change  a  fraction  to  higher  terms,  multi- 
ply both  numerator  and  denominator  by  a  num- 
ber that  will  give  the  denominator  desired. 

1.  Change  or  reduce  ^  to  35ths. 

Process 

35  --  5  =  7. 
1^  =  28.   ^^^^ 

5  X  ;r   35 

2.  Change  J ;  |  ;  |-  to  16ths. 

3.  Change  I;  |;  i-;  |- to  18ths. 

4.  Change!;  |;  -|;  i;  f;  35_to24ths. 

5.  Change  | ;  | ;  | ;  3-^^  to  32ds. 

6.  Changef;  j\;  l  ;  J;    |;  1;  ^-^  to  36ths. 

7.  Change  i ;  i ;  j ;  J ;  1^ ;  2%-  ^^  ^Oths. 


26  FUNDAMENTAL  OPERATIONS 

CHANGING   IMPROPER   FRACTIONS   TO   WHOLE 
OR  MIXED   NUMBERS 

36.  To  change  an  improper  fraction  to  a  whole 
or  mixed  number,  divide  the  numerator  by  the  de- 
nominator. 

1.  Reduce  y-  to  a  whole  or  mixed  number. 

Process 

^1- =  71 -=- 6  =  llf.   Ans. 

2.  Reduce  ^-^- ;  ^^~ ;  Jj-y^- ;  ^^-f-  to  whole  or  mixed 
numbers. 

3.  Reduce  ^^-;  ^^;  ^^- ;  -%\^-  to  whole  or 
mixed  numbers. 

4.  Change  ^^  lb. ;  Jj^^-  pk. ;  -%^^  miles ;  %^-  hr. 
to  mixed  numbers. 

5.  Change  ^^^-  bu. ;  ^^^-  yr. ;  ^^-  da.  to  mixed 
numbers. 

6.  Change  1^"^  pk. ;  ^p  lb.;  $\%^-;  $^ 
to  mixed  numbers. 


CHANGING    MIXED    NUMBERS    TO    IMPROPER 
FRACTIONS 

37.  To  change  a  mixed  number  to  an  improper 
fraction,  multiply  the  whole  number  by  the  de- 
nominator of  the  fraction,  add  in  the  numerator, 
and  write  the  sum  over  the  given  denominator. 


COMMON  FRACTIONS  27 

1.  Reduce  5f  to  an  improper  fraction. 

Process 

7 
35 

37,  that  is,  5|  =  ^.   Ans. 

2.  Reduce  261;  47f ;  67|;  32f  to  improper 
fractions. 

3.  Reduce  65f ;  S9^^;  257^^;  SM^  to  im- 
proper fractions. 

4.  Change  17|  to  ninths;  48|-  to  sevenths. 

5.  'Reduce  579^^;  iSl^^j-;  384^^  to  improper 
fractions. 

6.  Reduce  12353^;  527^^;  7 854^^  to  improper 
fractions. 

7.  Reduce  2721;  30^;  893-^g;  2 66 1  to  improper 
fractions. 

ADDITION    AND    SUBTRACTION    OF    FRACTIONS 
Least  Common  Multiple 

38.  The  large  number  of  fractions  we  meet  in 
ordinary  work  can  easily  be  reduced  to  a  common 
denominator  by  inspection,  but  if  the  denominators 
are  not  easily  reducible  the  following  method  is 
very  convenient  for  finding  the  least  common  mul- 
tiple. 


28  FUNDAMENTAL  OPERATIONS 

1.    Add  ^,  j\,  and  ^. 

Process 

2)  12     15     24  Explanation :  The  denomi- 

nators are  12,  15,  and  24. 

Arrange  them  as  here 
shown. 

Divide  by  any  prime  num- 
ber that  will  go  evenly  into 
any  two  or  more  of  them, 
bringing  down  any  numbers 
not  divisible. 

Repeat  this  until  no  two 
of  the  numbers  have  a  common  divisor. 

The  product  of  the  divisors  and  all  the  numbers  remain- 
ing will  be  the  least  common  multiple. 

Reduce   the   fractions  to  fractions  having  the  common 
denominator  120. 
Add  the  fractions. 
Reduce  the  improper  fraction  to  a  mixed  number. 

In  subtraction  of  fractions  follow  the  same  plan 
as  in  addition,  and  then  subtract  the  numerators. 


2) 

6     15 

12 

31 

3     15 

6 

1       5 

2 

2x 

2x3x5x2= 

120,  1.  c.  m. 

■^■■ 

=  i¥ir 

t\- 

—  32 

—  120 

5     . 

—     25 

T¥- 

—  TJ^ 

m- 

=  hh' 

,    Ans. 

From  |-  take  |. 


Process 


7  _  3  s 

2   —   16 


7_2_3  5_16   —   19         A.,^ 
¥5—111         Tff  —  TTF-     ^"'^• 

Addition  and  Subtraction  of  Fractions.  —  To 
add  or  subtract  fractions,  reduce  the  fractions 
to  a  common  denominator  and  add  or  subtract  the 
numerators. 


COMMON  FRACTIONS  29 

Written  Exercise 
39.    Perforin  the  operations  indicated  : 

1       1-^2.3  3      Xj_1_|.3    .    2 

^-      6  ^  8  ^  9  ^  3-  *■      9        3 

5.  24-|-  bushels  minus  15|-  bushels  =  ? 

6.  From  I  take  -^ ;  from  ^  take  ^q. 

7.  From  171  take  ^^,  from  19f  take  13|-. 

8.  From  41J  take  39|;  from  341  miles  take 
19|-  miles. 

^-      3^7         9^14-  ■^"-      8        6^5        10' 

Written  Problems 

^      40.   1.    From  a  car  of  40^  tons  of  coal,  29|  tons 
were  sold.     How  many  tons  remained  ? 

2.  From  33J  yards  of  cloth,  121  yards  and 
7^  yards  were  sold.     How  many  yards  were  left? 

3.  A  bin  contained  3541  bushels  of  wheat,  from 
which  216|  were  sold  and  29^  were  sowed.  How 
many  bushels  were  left  in  the  bin  ? 

4.  If  cream  contains  yBo^  protein,  ^|-  fat,  ^^q 
carbohydrates,  j^  salts,  and  the  rest  water,  find 
the  amount  of  water. 

5.  If  wheat  bread  contains  ^j  protein,  ^^  fat, 
J  carbohydrates,  xito"  salts,  and  the  rest  water, 
find  the  amount  of  water. 


30  FUNDAMENTAL  OPERATIONS 

tX  6.  If  a  man  devotes  ^-^  of  his  time  to  sleep,  ^ 
to  meals,  f  to  business,  how  much  of  his  time  is 
left  for  other  purposes  ? 

7.  After  an  automobile  had  been  driven  48J- 
miles,  50|  miles,  and  40|-  miles,  the  speedometer 
read  455|-  miles.  What  was  the  reading  at  the 
start? 

MULTIPLICATION    AND    DIVISION    OF 
FRACTIONS 

Study  Exercise 

41.  In  multiplication  of  fractions  multiply  the 
numerators  together  for  a  new  numerator,  and  the 
denominators  together  for  a  new  denominator. 
Reduce  the  resulting  fraction  to  its  lowest  terms. 
Employ  cancellation  whenever  possible.  In  divi- 
sion invert  the  divisor  and  proceed  as  in  multipli- 
cation. 

An  indicated  division  in  which  one  or  both  terms 
are  fractions  is  called  a  complex  fraction. 

In  multiplication  of  fractions  do  not  multiply 
the  terms  until  all  the  like  factors  have  been 
canceled. 

1.    Multiply  ^  by  f. 

Process 

^   ;r    4 

4 


COMMON  FRACTIONS  31 

2.    Multiply  4f  by  5f . 

Process 

In  division  invert  the  divisor  and  proceed  as  in 
multiplication. 

2 


3.    Divide  f  by  3. 


Process 
4 


8^2^§     ^=1     A 
9  "3     ^^^     3'      ^^' 
3 

4.   Divide  6 J  by  2|. 

Process 


49^14^^      5  ^35 
8    ■   5       8      ;4     16 


H-^^=^^^  =  ^Xil  =  ^=^T\-   ^«*- 


Written  Exercise 

42.  Perform  the  operations  indicated  : 

1.  Multiply  f  by  7  ;  iV  by  4  ;  f  by  9. 

2.  Multiply  I  by  I;  A  by  f ;  |  by  f . 

3.  ^Multiply  6|  by  8  ;  IT^V  by  18  ;  19 j%  by  ii. 

4.  Multiply  24f  by  1 ;  IS^^^  by  A  5  4^  by  11- 

5.  Multiply  16J  by  4| ;  251  by  Tf ;  47|  by  9f . 

6.  Divide  13  by  3^3- ;   T  by  3^ ;  I  by  3^. 


a2  FUNDAMENTAL  OPERATIONS 


10. 


15. 


Divide  13  by  f;  f  by  | ;  ^V  by  2f 

Divide  Hi  by  lOJ;  |  by  7i. 

Divide  f  of  81  by  |  of  17^. 

16             ^1             1^             123. 
f              A              5              161 

27i 

14.            2 

40| 

301 

/5XA      le     ^^*      17    l^J"^ 
1x1  •        •    4i-            311+8- 

5 

20 

Written  Problems 

43.   1.    If  100  pounds  of  milk  produce  5|  pounds 
of  butter,  how  much  will  a  pound  of  milk  produce  ? 

2.  With  the  same  production  as  in  problem  1, 
how  much  butter  will  a  cow,  giving  four  gallons  of 
milk  a  day,  produce  if  the  milk  weighs  8|  pounds 
per  gallon  ? 

3.  A  dressed  hog  weighs  308  pounds  which  is 
I  of-  the  live  weight.     What  was  the  live  weight  ? 

4.  A  train  running  from  Baltimore  to  Cumber- 
^land  makes  the  distance  of  192 J  miles  in  4J  hours. 

What  is  the  rate  per  hour  of  the  train  ? 

5.  If  a  dry  gallon  contains  268|  cubic  inches, 
how  many  cubic  inches  do  94|-  dry  gallons  contain  ? 

6.  A  merchant  buys  the  following  bill  of  goods  : 
cotton  goods  $235.70,  silk  $361.85,  and  carpets 

(/  $458.50.     He  receives  a  discount  of  \  of  the  bill 
for  cash.     What  does  he  pay  for  the  goods  ? 


COMMON  FRACTIONS  33 

7.  If  it  requires  7j  acres  of  corn  to  fill  a  98-ton 
silo,  what  fractional  part  of  the  silo  will  one  acre 
fill? 

8.  If  a  normal  child  at  birth  has  a  chest  meas- 
urement of  13 1-  inches  and  at  4  years  of  age  of 
20|^  inches,  what  is  the  average  yearly  increase  in 
chest  measurement? 

9.  If  a  man  w^orking  7^  hours  a  day  can  com- 
plete a  piece  of  work  in  16|^  days,  how  many  hours 
must  he  work  per  day  in  order  to  complete  the 
same  work  in  14^  days,  working  at  the  same  rate? 

10.  If  a  loom  weaves  60  yards  of  cloth  in  12^ 
hours,  how  many  yards  are  woven  in  an  hour  ? 
How  long  will  it  take  to  weave  165  yards  ? 


Review  Written  Ex< 

Brcise 

44 

•    1-    l  +  f  +  f  +  t=? 

2. 

6|+2f +43-^^+81=? 

3. 

25f  +  16|-12f=  ? 

4. 

75^+57f-46i-21i=  ? 

5. 

"9  ^  1  6"  ^  8  ^  "9  —    • 

6. 

5fx3fx7i=? 

7. 

1501-^221=  ? 

8. 

70|x33ix24f=  ? 

9. 

3^4 

^    '    ''      .                                        10. 

31  +  21 

4*- 
81- 

-^ 

-H 

34  FUNDAMENTAL  OPERATIONS 

Review  Written  Problems 

45.  1.  A  bank  teller  received  during  the  day 
$  3285  in  silver  and  paper  money.  There  was  f 
as  much  silver  as  paper  money.  How  much  of 
each  did  he  receive  ? 

2.  A  merchant  bought  37 J  pounds  of  coffee  for 
$14.25;  if  he  had  paid  2|j^  less  a  pound,  how 
many  pounds  would  he  have  received  ? 

3.  If  a  farm  is  ^  in  corn,  2F  i^  wheat,  ^  in 
oats,  J  in  pasture,  ^^q-  in  timber,  and  the  remaining 
6f  acres  is  occupied  by  buildings,  yards,  etc.,  what 
is  the  size  of  the  farm,  and  how  many  acres  are  in 
each  division? 

4.  A  farmer  mixed  a  ton  of  fertilizer  for  his 
corn  land,  using  ^  cottonseed  meal  at  $  30.50  a  ton 
and  J|-  and  -^  of  the  rest  acid  phosphate  and 
muriate  of  potash  respectively.  The  acid  phosphate 
cost  $15.25  a  ton  and  the  potash  $45.50  a  ton. 
What  did  the  fertilizer  cost  ? 

5.  Three  pipes  can  empty  a  reservoir  in  5J,  4, 
and  3|  hours  respectively.  How  long  will  it  take 
them  running  together  ? 

6.  If  a  man  by  working  5^  hours  a  day  can 
complete  a  piece  of  work  in  9J  days,  how  many 
hours  must  he  work  per  day  to  complete  the  work 
in  7  days  ? 


COMMON  FRACTIONS  35 

7.  If  it  requires  4|-  acres  of  corn  to  fill  a  65-ton 
silo,  how  many  acres  will  it  require  to  fill  a  90-ton 
silo? 

8.  If  one  cow  requires  31  cents  worth  of  feed  to 
produce  IJ  pounds  of  butter  fat  and  a  second  cow 
produces  1  pound  for  16^^,  what  fraction  of  the 
feed  required  by  the  first  cow  is  sufficient  for  the 
second  ? 

9.  If  an  apple  tree  bears  2781  apples  and  J  are 
windfalls,  and  ^  of  the  remaining  are  wormy,  what 
fraction  of  the  apples  is  good  ?  What  is  the  num- 
ber of  good  apples  ? 

10.  A  farmer  bought  15^  bushels  of  clover  seed 
containing  |-  bushel  of  poor  seed  for  $8.25  per 
bushel.  What  was  the  total  cost  of  the  seed? 
How  much  per  bushel  for  the  good  seed  ? 

11.  A  merchant  bought  250  baskets  of  peaches 
at  37|^^  a  basket.  He  sold  |  of  them  at  an  ad- 
vance of  10  ^  a  basket,  ^  of  the  remainder  at  35  ^ 
a  basket,  and  the  remainder  at  a  loss  of  5J^  a 
basket.     What  did  he  gain  or  lose  ? 

12.  If  4-  of  the  value  of  a  farm  is  $4360,  what 
is  J  of  the  farm  worth  ?  li  ^  and  -|-  of  the  farm 
are  deeded  to  heirs,  what  is  the  value  of  the  part 
remaining  ? 


DECIMAL   FRACTIONS 
Study  Exercise 

46.  A  decimal  fraction  is  a  fraction  whose  de- 
nominator is  ten  or  a  multiple  of  ten. 

The  denominator  is  usually  not  written,  but  the 
denomination  is  indicated  by  the  position  of  the 
decimal  point.     Thus  :  yo  =  -^  ',  xw  ~  •^^• 

The  decimal  point  separates  the  whole  number 
from  the  fraction.     Thus  :  2.57  ;  76.039. 

The  first  place  to  the  right  is  tenths  ;  the  second, 
hundredths ;  and  the  third,  thousands,  etc. 

A  pure  decimal  is  one  containing  neither  a  whole 
number  nor  a  common  fraction ;  as,  .587. 

A  mixed  decimal  is  one  containing  a  whole 
number  and  a  decimal ;  as,  76.39. 

A  complex  decimal  is  one  which  ends  with  a 
common  fraction  ;  as,  .57^. 

Fundamental  principles  involved  in  decimals : 

(1)  If  the  decimal  point  is  moved  to  the  right,  the 
niunber  is  multiplied  by  10  for  each  place  the  point 
is  moved. 

Thus:  .765x10=7.65. 

(2)  If  the  decimal  point  is  moved  to  the  left,  the 
nimiber  is  divided  by  10  once  for  each  place  the 
point  is  moved. 

Thus:  .765 ^10  =  .0765. 

36 


DECIMAL  FRACTIONS  37 


Oral  Exercise 

47. 

Read  the 

following : 

1. 

.6. 

5.    .5365.                9.    1.001. 

2. 

.53. 

6.    .206.                10.    10.10. 

3. 

.325. 

7.    12.12.              11.   43.0043. 

4. 

.03. 

8.   205.205.          12.   808.08. 

13. 

57.00057. 

16.    72.0001. 

14. 

.000789. 

17.   8.009981 

15. 

7007.707. 

18.   26,000.00026. 

COMMON   AND    DECIMAL   FRACTIONS 

48.  Common  fractions  may  be  reduced  to  deci- 
mals, and  decimals  to  common  fractions. 

To  reduce  a  common  fraction  to  a  decimal,  an- 
nex ciphers  to  the  numerator  and  divide  by  the 
denominator. 

1.  Reduce  |-  to  a  decimal. 

Process 

i  X  HI  =  tVtAt  =  -125  Ans.  or  8)L000 

.125  Ans. 

To  reduce  a  decimal  to  a  common  fraction,  write 
the  fraction  with  its  denominator  and  reduce  it  to 
its  lowest  terms. 

2.  Reduce  .375  to  a  common  fraction. 

Process 


38  FUNDAMENTAL  OPERATIONS 

Written  Exercise 

49.  1.  Reduce  .25;  .75;  .625;  .875;  .275  to 
common  fractions. 

2.  Reduce  .33^;  .66|;  .83J;  .16|  to  common 
fractions. 

3.  Reduce  5.875;  32.0225;  5.625;  75.015; 
300.05  ;  210. 3J  to  common  fractions. 

4.  Reduce  f ;  J ;  | ;  f ;  3-V  5  ^^^  T2  ^^  decimals. 

5.  Reduce  f ;  3^ ;  3^2  >  A  5  ^^^  2*6  ^^  decimals. 

6.  Reduce  3^ ;  3^ ;  ^ ;  3^ ;  and  f^  to  decimals. 

7.  Reduce  6J;  16J;  98f ;  7J;  53-^g-  to  mixed 
decimals. 

ADDITION    AND    SUBTRACTION    OF    DECIMALS 

50.  Since  the  units,  tens,  etc.,  are  to  the  left  of 
the  decimal  point,  and  the  tenths,  hundredths,  etc., 
are  to  the  right  of  the  decimal  point,  it  follows 
that  to  add  decimals  the  numbers  must  be  written 
so  that  the  decimal  points  lie  in  a  vertical  line ; 
i.e.,  so  that  the  different  denominations  come  in  the 
same  column.  The  addition  should  be  performed 
as  in  addition  of  whole  numbers.  The  same  rule 
as  regards  the  decimal  point  also  applies  to 
subtraction. 

Add  25.2;  32.07;  56.255;  125.0125;  7.8;  and 
34.65. 


DECIMAL  FRACTIONS  39 

Process 

25.2 

32.07  Explanation:    Arrange   the   addends   in 

56.255  form   for  addition,   keeping   the   decimal 

125.0125  points  in  vertical  line,  so  as  to  keep  units 

7.8  under  units,  tens  under  tens,  etc.     Add. 
34.65 


280.9875   Ans. 


Written  Exercise 


51.  Perform  the  operations  indicated.  Check 
the  results : 

1.  Add  6.789;  1.067;  .024;  .65;  17.005; 
.0046;  1.035;  1.0706;  24.018. 

2.  From  234.096  take  74.16  ;  from  13.435  take 
.306  ;  from  41  take  35.067. 

3.  From  .9  take  .0652;  from  765.789  take 
34.908. 

4.  From  1001.0897  take  8.0907;  from  .235 
take  .0007. 

5.  From  6000.0873  take  754.0001;  from 
21.3004   take    17.017. 

6.  From  $  154.75  take  $  19.48  ;  from  $  1010.20 

take  $524.38. 

7.  From  707.413  take  90.00019  ;  from  17.00017 
take  8.378. 

8.  From  ten  thousand  ten  and  one  hundred  one 
thousandths  take  nine  hundred  nine  and  nineteen 
hundred-thousandths. 


40  FUNDAMENTAL  OPERATIONS 

9.    From  503.458  take  189.0009  ;  from  784.009 
take  229.0009. 

10.  From  $1235.65  take  $825.35;  from 
$3727.84  take  $1779.87. 

11.  From  three  thousand  three  and  seven  hun- 
dred sixty-five  thousandths  take  two  thousand  one 
and  seventy-seven  ten-thousandths. 

.  12.    .5007 +  .7068 +  .70007 +  406.1295 +46.008 
-86.1745-.005274  =  ? 

13.  3.8  +  743.65  +  .08  +  .00306  +  .863  + 14.7436 

14.  7.63427  +  8.0907  -  2.054  +  .0601  +  24.018 
=  ? 

15.  72.61+ 23.561  + 18.371- 29.6|=  ? 

16.  83.311  +  32.768f  +  40.121  -  61.17|  =  ? 


17.  69.171- 38.16f- 20.81  + 12.06|  =  ? 

18.  78.041  +  97.40^  -  37.78|  -  26.161  =  ? 


19.  3.015f  +  .86|+  .007|+  .78i+.0085f +2.8f 
+  .9f  =  ? 

Written  Problems 

52.  1.  The  rainfall  at  Geneva,  N.  Y.,  for  1913, 
from  January  to  December  inclusive,  was  as 
follows:  3.88  in. ;  .11  in. ;  4.6  in. ;  3.40  in. ;  2.68 
in.;  3.24  in.;  2.03  in.;  1.65  in  ;  2.64  in.;  4.03 
in.;  2.41  in.;  .77  in.  What  was  the  total  rain- 
fall? 


DECIMAL  FRACTIONS  41 


2.  The  above  illustration  shows  butcher's  cuts 
and  their  relative  weights.  The  live  weight  of  the 
animal  was  1733;  the  dressed  weight  of  the  carcass 
is  how  many  pounds  ?  What  is  the  value  at  the 
following  prices:  neck,  12J^  ;  chuck,  15^;  prime 
of  rib,  16^;  porterhouse,  22^ i^ ;  sirloin,  22^-^; 
rump,  15^;  round,  20^;  plate,  10^;  flank,  15^; 
shank,  8^  ;  and  shin,  8j^  ? 

3.  The  labor  expenses  in  producing  an  acre  of 
corn  were:  shelling  seed,  $.03;  plowing,  $1.31; 
dragging,  $  .54;  planting,  $  .24  ;  cultivating,  $  1.81; 
husking,  $3.46.     What  was  the  total  expense? 

4.  A  chemical  analysis  of  a  package  of  butter 
weighing  16.7  ounces  showed  13.8  ounces  of  fat, 
.15  ounce  of  casein,  .46  ounce  of  salt,  and  the  rest 
water.     What  was  the  amount  of  water  ? 


42  FUNDAMENTAL  OPERATIONS 

5.  Tf  in  100  pounds  of  alfalfa  meal  there  are  9.1 
pounds  of  water,  9.5  pounds  of  ash,  26.6  pounds 
of  fiber,  36.8  pounds  of  nitrogen,  2.1  pounds  of 
fat,  and  the  rest  protein,  how  mueh  protein  is  there  ? 

MULTIPLICATION  AND  DIVISION   OF  DECIMALS 

53.  In  multiplication  of  decimals  proceed  as  in 
whole  numbers,  jand  then  point  off  as  many  places 
in  the  product  as  there  are  places  in  both  the  mul- 
tiplier and  multiplicand. 

In  division,  after  dividing  as  in  whole  numbers, 
point  off  as  many  places  in  the  quotient  as  the  num- 
ber of  places  in  the  dividend  exceeds  the  number  in 
the  divisor.  If  there  are  fewer  places  in  the  divi- 
dend than  in  the  divisor,  add  a  sufficient  number  of 
ciphers  to  make  the  number  of  places  the  same. 

Simplify  the  process  by  making  the  divisor  a 
whole  number. 

1.   Divide  43.051  by  .314. 

Process 


137.10 
/314 1 43/051.00 
314 
1165 
942 


2231 
2198 


330 
314 
160 


Explanation :  Change  the  decimal  divisor 
to  a  whole  number  by  moving  the  point 
three  places  to  the  right.  Move  the  point 
in  the  dividend  to  the  right  the  same  num- 
ber of  places.  Cross  out  the  old  points. 
Divide. 


DECIMAL  FRACTIONS  43 

Written  Exercise 

54.  Perform   the   operations   indicated.     Check 
the  results. 

1.  Multiply  246.324  by  .172. 

2.  Multiply  .00086  by  45.3. 

3.  Multiply    324.547     by    7.32;     789.67     by 
394.835. 

4.  Multiply  70.08754  by  6.875  ;  .0656  by  4.2. 

5.  Multiply  54.785  by  .002 ;  765.53  by  .0634. 

6.  Divide  25.25  by  .25  ;  73.731  by  .0003. 

7.  Divide  .000875  by  125;  .0101  by  101. 

8.  Divide  3243  by  .0001 ;  742.303  by  .6. 

9.  Multiply  1.017  by  1.2  ;  4235.5  by  562.74. 

10.  Divide  2.4  by  .0008;  523.546  by  4325.08. 

11.  Multiply  117.11  by  31.01;  690.007  by  9.004; 
.7854  by  36. 

12.  Multiply  3.1416  by  38.62;  2.7818  by  .7447; 
6069.06  by  .00346. 

13.  Multiply    15.371    by    21.081;     28.72f    by 
45.66f ;  .19.6f  by  .0371 

14.  Divide     125.421     by     26.61;     86.16 J     by 
12.171;  92.28|by  5.831 

Written  Problems 

55.  1.  What  will  15,850  bricks  cost  at  $  6.75  per 
thousand  ? 

2.   What  will  5484  feet  of  lumber  cost  at  %  4.25 
per  thousand  feet  ? 


44  FUNDAMENTAL  OPERATIONS 

3.    What  will  2750  pounds  of  hay  cost  at  $  14.50 
per  ton  ? 
w/  4.  What  is  a  load  of  4110  pounds  of  coal  worth 
at  $4.50  per  ton? 

5.  What  is  the  value  of  38  barrels  of  apples  at 
$  4.50  per  barrel  ? 

6.  (JWhat  is  7463  pounds  of  corn  worth  at  95)^  a 
hundred. 

7.  One  bushel  of  wheat  occupies  about  .8  of  a 
cubic  foot  of  space.  How  many  bushels  in  a  bin 
that  contains  478.75  cubic  feet  ? 

8.  Find  the  cost  of  3125  pounds  of  com  meal  at 
$  3.15  a  hundred. 

^   9.    What  is  the  freight  on  a  bill  of  goods  weigh- 
ing 3185  pounds  at  85^  a  hundred? 

10.  A  load  of  wheat  weighs  1875  pounds  net. 
What  is  its  value  at  $  1.12  a  bushel  ? 

ALIQUOT  PARTS  APPLIED  TO  MULTIPLICATION 
AND  DIVISION 

56.  An  aliquot  part  is  a  simple  fractional  part  of 
100.  Those  most  commonly  used  are :  50,  or  \  of 
100 ;  25,  or  \  of  100  ;  33i  or  \  of  100  ;  10  or  ^^ 
of  100  ;  81,  or  j-V  of  100 ;'  6J,  or  J^  of  100. 

1.  14f  is  what  part  of  100? 

2.  40  is  what  part  of  100  ? 

3.  75  is  what  part  of  100  ? 

4.  60  is  what  part  of  100  ? 


DECIMAL  FRACTIONS  45 

5.  80  is  what  part  of  100  ? 

6.  371  is  what  part  of  100  ? 

7.  311  is  what  part  of  100? 

8.  621  is  what  part  of  100  ? 

9.  871  is  what  part  of  100  ? 

10.  66-|  is  what  part  of  100  ? 

11.  41|  is  what  part  of  100  ? 

12.  831  is  what  part  of  100? 

13.  581  is  what  part  of  100  ? 

14.  125  is  what  part  of  100  ? 

15.  150  is  what  part  of  100  ? 

16.  175  is  what  part  of  100  ? 

57.  To  multiply  a  number  by  any  one  of  the 
aliquot  parts,  first  multiply  by  100  by  annexing  two 
ciphers,  then  by  the  fractional  part  the  number  is 
of  100. 

1.    Multiply  480  by  25. 

Process  Explanation :  To  multiply  by  25,  first 

480  X  100  multiply  by  100,  and  since  25  is  ^  of 

=  12,000    100   take  ^  of   the  product.     In   this 

process,  do  not  cancel  4  into  100. 

To  divide  a  number  by  an  aliquot  part,  first 
divide  the  number  by  100  and  then,  since  the 
quotient  is  the  result  of  dividhig  by  a  number  that 
is  larger  than  the  number  to  be  used  as  a  divisor, 
multiply  the  result  by  the  fractional  part  (inverted) 
the  divisor  is  of  100. 


46  FUNDAMENTAL  OPERATIONS 

2.   Divide  480  by  25. 

Process  Explanation:  To  divide  a  number  by  25, 

480  X  4  ^^^^  divide  the  number  by  100.     Now,  since 

— 7qq~"  =  ^^-  the  divisor  is  4  times  as  great  as  25,  the  re- 
sult will  only  be  \  as  much  as  it  should  be ; 
hence,  multiply  by  four  to  obtain  the  result  required. 

Written  Exercise 

58.  Perforin  the  operations  indicated,  using  the 
aliquot  parts  method  when  possible. 

1.  Multiply  and  divide  936,  876,  3647,  1357, 
4321  by  121   16f ,  331 

2.  35  is  what  part  of  95  ? 

3.  17  is  what  part  of  68  ? 

4.  221  is  what  part  of  80  ? 

5.  321  is  what  part  of  120  ? 

6.  16|  is  what  part  of  37J  ? 

7.  671  is  what  part  of  150  ? 

8.  41 J  is  what  part  of  601  ? 

9.  78J  is  what  part  of  96|  ? 
10.    50|  is  what  part  of  75J  ? 

Written  Problems 

59.  1.    What  are  18  pounds  of  coffee  worth  at 
25  ^,  at  331  ^^  at  37^  ^,  per  pound  ? 

2.  What  will  96  rods  of  wire  fence  cost  at  66|  ^ 
per  rod  ? 

3.  What  rent  will  a  man  pay  for  a  section  of 
land  at  $  6  J  per  acre  ? 


DECIMAL  FRACTIONS 


47 


4.  "What  will  be  received  for  a  40-gallon  can  of 
milk  at  8 J  ^  per  quart  ? 

5.  A  drover  paid  $  825  for  cattle  at  $  37.50  a 
head.     How  many  did  he  buy? 

6.  What  is  the  value  of  42  cars  of  coal  averag- 
ing 37-J  tons  each  at  $  3.87|-  a  ton  ? 

7.  Find   the  cost  of    795  miles  of   railroad   at 
$  6250  a  mile. 

8.  How  many  pounds  of  fertilizer  at  $  .83 J  per 
hundredweight  can  be  bought  for  $  15.50  ? 

9.  How  many  feet  of  lumber  at  $  31.25  per  M 
can  be  boupfht  for  $  165  ? 


REVIEW    OF   DECIMALS    AND    COMMON 
FRACTIONS 

Written  Exercise 
60.   The  following  table  shows  the  effect  of  con- 
tinuous cropping,  with  and  without  manuring. 
{From  the  Bothamsted,  Hertfordshire,  England.) 


Ybar 

Bushels  op  Wheat 
PER  Acre 

BuBiiELS  OP  Barley 
PER  Acre 

Unmanured 

Manured 

Unmanured 

Manured 

1844-'51 

1852-'o9 

1860-'67 

1868-75 

1876-'83    ..... 

1884-'91 

1892-'9:3 

17f 
161 

12| 
9^ 

28 

34J 
35| 
35| 
28| 
39  i 
33| 

241 
18 
14^ 
141 

111 
lOf 

44i 
32| 
49i 
52i 
44f 
49^ 

48  FUNDAMENTAL  OPERATIONS 

1.  What  was  the  total  yield  of  wheat  on  the 
unmanured  field  ?     The  total  barley  yield  ? 

2.  What  was  the  total  yield  of  wheat  on  the 
manured  field  ?     The  total  yield  of  barley  ? 

3.  Determine  the  average  yield  per  year  for  each 
of  the  columns  given  above. 

Written  Problems 

61.  1.  If  the  average  yield  of  wheat  in  Kansas 
is  13.7  bushels,  what  is  the  value  of  the  wheat  at 
95^  per  bushel? 

2.  If  it  costs  $9.34  to  produce  an  acre  of 
wheat,  what  is  the  average  profit  to  the  wheat 
grower  in  Kansas  ?  If  the  average  were  increased 
to  31  bushels  (the  average  for  Great  Britain),  what 
would  be  the  profit  in  raising  wheat  in  Kansas  ? 

3.  If  .025  of  the  seed  wheat  used  to  sow  an 
80-acre  field,  five  pecks  to  the  acre,  was  weed  seed, 
how  many  pecks  of  the  seed  were  weed  seed  ? 
How  many  acres  were  sowed  to  weeds  ? 

4.  If  alfalfa  seed  is  $  9  per  bushel,  what  is  the 
price  per  bushel  for  pure  seed  if  .23  of  the  seed  is 
weed  seed  ? 

5.  If  clover  seed  is  $  7.50  per  bushel  and  .17 
of  the  seed  is  weed  seed,  and  a  germination  test 
showed  that  2  out  of  every  25  of  the  pure  seed  will 
not  germinate,  what  is  the  cost  per  bushel  for  good 
seed? 


J^ 


DECIMAL  FRACTIONS  49 

6.  A  man's  time  is  worth  30  ^  per  hour.  What 
is  it  worth  to  treat  150  bushels  of  wheat  with  a 
solution  for  killing  smut  spores,  if  20  bushels  of 
seed  can  be  treated  in  an  hour  ? 

7.  If  a  farmer  pays  $  3  for. a  smut  cure  treat- 
ment, and  if  the  yield  on  120  acres  of  wheat  is 
increased  6  bushels  per  acre  thereby,  what  is  his 
increased  profit  per  acre  if  wheat  is  worth  95  j^  per 
bushel  ? 

8.  The  mixture  to  kill  smut  spores  in  wheat  costs 
50  ^  for  40  bushels.  If  1^  bushels  of  wheat  are  sown 
to  the  acre,  what  will  the  solution  cost  per  acre  ? 

9.  If  it  costs  %  10.44  per  acre  to  produce  a  crop 
of  corn  and  husk  it  from  the  standing  stalks,  what 
does  it  cost  to  produce  a  bushel  of  corn  when  the 
yield  is  60  bushels  per  acre  ?  40  bushels  per  acre  ? 
75  bushels  per  acre  ? 

10.  If  it  costs  $  5.50  per  acre  to  produce  a  crop 
of  2.5  tons  of  clover  hay,  how  much  does  it  cost  to 
produce  a  ton  of  clover  hay  ? 

11.  If  corn  is  worth  40  ^  a  bushel  (56  lb.)  and 
clover  hay  %  8  per  ton,  what  will  it  cost  per  day  to 
feed  a  horse  10  pounds  of  com  and  14  pounds  of 
clover  hay  ? 

12.  If  bran  is  $  24  a  ton,  corn  60  ^  per  bushel, 
and  hay  $  9  per  ton,  what  will  be  the  cost  of  a 
day's  feed,  consisting  of  8  pounds  of  bran,  6  pounds 
of  corn,  and  16  pounds  of  hay  ? 


50  FUNDAMENTAL  OPERATIONS 

13.  What  will  it  cost  to  feed  a  horse  16  pounds 
of  hay  and  5  pounds  of  oats,  if  hay  is  worth  $  9 
per  ton  and  oats  are  worth  37  ^  per  bushel  (45  lb.)  ? 
If  the  above  is  the  average  feed  per  day  for  a  horse 
at  light  work,  what  will  it  cost  to  keep  a  horse 
a  year  ? 

14.  What  is  the  cost  of  3.2  pounds  of  corn  stover 
and  10  pounds  of  hay,  if  com  stover  is  $  4  per  ton 
and  clover  hay  $  9  per  ton  ? 

15.  A  cow  eats  3.5  tons  of  hay  worth  $7  per 
ton,  1200  pounds  of  ground  feed  worth  90^  per 
hundred,  and  pasture  amounting  to  $  8.  What 
will  it  cost  to  keep  a  cow  a  year  ? 

16.  An  ordinary  cow  will  give  13  pounds  of 
milk  per  day  for  300  days  in  the  year.  If  .042  of 
the  milk  is  butter  fat,  what  will  be  the  gross 
receipts  from  the  cow  with  the  butter  fat  averaging 
29  )^  per  pound  ? 

17.  A  carefully  selected  Jersey  cow  will  give  24 
/  pounds  of  milk  per  day  for  325  days  in  the  year. 

If  .053  of  the  milk  is  butter  fat,  what  will  be  the 
gross  receipts  from  this  cow  ?  Compare  with 
Problem  16. 

18.  A  sample  of  fresh  milk,  tested  by  the  Bab- 
cock  test,  showed  that  .0364  of  the  milk  was  but- 
ter fat.  After  the  milk  was  set  away  in  shallow 
pans  for  12  hours  and  then  skimmed,  the  test 
showed  that  .0044  of  the  skimmed  milk  was  butter 


DECIMAL  FRACTIONS  51 

fat.     What  fraction  of  the  butter  fat  was  left  in 
the  skimmed  milk  ? 

19.  Another  sample  of  the  same  milk  is  set 
away  in  deep  pans  for  the -Same  time,  and  the 
skimmed  milk  showed  that  only  .0017  of  the  milk 
was  butter  fat.  What  fraction  of  the  butter  fat 
was  lost  ? 

20.  After  using  a  hand  separator  on  another 
sample  of  the  milk,  .0002  of  the  skimmed  milk 
was  butter  fat.  What  fraction  of  the  butter  fat 
was  lost  ? 

21.  Maid  Henry,  of  the  Kansas  State  Agricul- 
tural College,  the  world's  champion  fourteen-year- 
old  cow,  gave  19,600.4  pounds  of  milk,  of  which 
.0364  was  butter  fat.  What  would  have  been  the 
number  of  pounds  lost  if  the  shallow-pan  system 
of  separating  the  cream  had  been  used  ?  What 
would  have  been  the  value  of  the  butter  fat  at  29^ 
per  pound  ? 

22.  What  would  have  been  the  loss  if  the  deep- 
pan  system  had  been  used  ?  What  would  have 
been  the  value  of  the  butter  fat  at  29  ^  per  pound  ? 

23.  What  would  have  been  the  loss  in  pounds, 
and  in  value  at  29  i^  per  pound,  if  the  hand  separa- 
tor had  been  used  ? 

24.  How  long  would  it  take  to  save  the  price  of 
a  $  55  separator  if  the  shallow-pan  system  were 
used  ?     If  the  deep-pan  system  were  used  ? 


52  FUNDAMENTAL  OPERATIONS 

25.  One  hundred  pounds  of  corn  contain  about 
1.58  pounds  of  nitrogen,  .37  pound  of  potash,  and 
.57  pound  of  phosphorus.  How  much  of  each  of 
these  elements  does  a  crop  of  50  bushels  (70  lb.) 
remove  from  the  soil  ? 

26.  Forty  analyses  of  soils  from  different  parts 
of  the  United  States  showed  an  average  of  3000 
pounds  of  nitrogen,  4000  pounds  of  phosphorus, 
and  16,000  pounds  of  potash  per  acre.  If  a  crop 
of  13.8  bushels  of  wheat  removes  14.5  pounds  of 
nitrogen,  10.6  pounds  of  phosphorus,  and  14 
pounds  of  potash  from  the  soil,  how  many  crops 
of  wheat  could  be  produced  if  all  the  nitrogen  were 
available  ?  If  all  the  phosphorus  were  available  ? 
If  all  the  potash  were  available  ? 

27.  For  every  ton  of  wheat  sold  from  the  farm 
it  is  estimated  that  the  farmer  sells  $  8.35  worth 
of  fertility,  and  for  every  ton  of  corn  $  6.50  worth. 
What  is  the  value  of  the  plant  food  removed  from 
the  soil,  if  he  raises  and  sells  860  bushels  of  wheat 
and  1134  bushels  of  corn  ? 

28.  The  Wisconsin  Experiment  Station  bulletin 
reports  that  by  using  20  tons  of  manure  upon  an 
acre  of  ground  7420  pounds  of  hay  were  produced,  by 
using  10  tons  4350  pounds  were  produced,  and  by  not 
using  any  at  all  only  2330  pounds  were  produced. 
Which  acre  yielded  the  greater  profit,if  the  manure  is 
valued  at  $1  per  ton  and  hay  is  worth  $18  per  ton  ? 


DECIMAL  FRACTIONS  53 

29.  In  a  block  of  Ben  Davis  apple  trees  at  the 
Kansas  State  Agricultural  College  not  sprayed, 
834  of  the  1769  apples  produced  were  affected 
with  the  blotch.  What  fraction  of  the  apples 
was  affected  ?     What  decimal  fraction  ? 

30.  In  another  block,  sprayed  with  lime  and 
sulphur,  960  of  the  3675  produced  were  affected. 
What  fraction  of  the  apples  was  affected  ?  What 
decimal  fraction  ? 

31.  In  another  block,  sprayed  with  a  3-4-50 
Bordeaux  mixture,  2438  apples  were  produced  and 
50  were  affected  with  the  blotch.  What  frac- 
tion of  the  apples  was  affected  ?  What  decimal 
fraction  ? 

32.  A  person  who  owned  |-  of  a  coal  mine  sold 
I"  of  his  share  for  $  12,380.  What  was  the  entire 
value  of  the  mine  ? 

33.  A  farmer  exchanged  32  bushels  of  potatoes 
@  67^^  per  bushel  for  sugar  at  19  pounds  for  $  1. 
How  many  pounds  of  sugar  did  he  receive? 

34.  A  man  invested  |-  of  his  money  in  land,  |  of 
the  remainder  in  a  house,  f  of  what  was  then  left 
in  bonds,  and  had  $  765  left.  How  much  money 
had  he  at  first  ? 

35.  If  the  freight  from  St.  Louis  to  Chicago  is 
44 (^  per  hundred  pounds,  what  must  be  paid  on 
four  boxes  of  goods,  weighing  respectively  269.4, 
365.5,  437.25,  and  341.25  pounds  ? 


54  FUNDAMENTAL  OPERATIONS 

36.  A  dealer  in  Boston  retails  coal  at  $8.25  per 
ton.  If  a  ton  costs  $  4.15  at  the  mine,  and  the 
freight  is  65  ^,  what  is  the  dealer's  profit  on  9260 
pounds  of  coal  ? 

37.  A  grocer's  sales  on  sugar  and  coffee  on  a 
certain  day  amounted  to  $  302.94.  He  sold  the 
same  number  of  pounds  of  each,  the  sugar  at  16 
pounds  for  a  dollar,  and  the  coffee  at  32  ^  per 
pound.     How  many  pounds  of  each  did  he  sell  ? 

38.  A  mower  costing  $41  and  cutting  on  the 
average  28  acres  a  year,  will  last  about  14.8  years. 
The  repair  charges  are  $26.94  and  the  interest  on 

^the  money  invested  is  $19.39.  If  actually  used 
46  days  during  its  life,  what  is  the  cost  of  the 
mower  per  day  used  ?  per  acre  cut  ? 

39.  A  binder  costing  $  125  and  cutting  35.2 
acres  annually,  lasts  about  15.4  years.  The  repair 
"charges  are  $31.20  and  the  interest  on  the  invest- 

K  ment  is  $61.60.  If  actually  used  53  days  during 
its  life,  what  is  the  cost  of  the  binder  per  day 
used  ?   per  acre  cut  ? 

40.  What  ,will  it  cost  to  feed  a  horse  4  pounds  of 
oats,  6  pounds  of  corn,  4  pounds  of  bran,  and  12 
pounds  of  hay,  if  oats  are  worth  42  ^  a  bushel,  corn, 
45^  a  bushel,  bran,  $1.15  a  hundred,  and  hay, 
$9.50  a  ton?  If  the  above  is  the  average  amount 
of  feed  per  day  for  a  horse  at  heavy  work,  what 
will  it  cost  to  keep  a  horse  a  year  ? 


/ 


FARM  ACCOUNTS 

Study  Lesson 

62.  Almost  every  up-to-date  farmer  finds  it 
necessary  to  keep  accurate  accounts  of  his  daily, 
weekly,  monthly,  and  yearly  business  transactions. 
The  farmer  may  feel  that  he  is  making  some  money 
from  year  to  year,  yet  unless  he  keeps  accounts  he 
will  not  know  how  much,  nor  just  what  is  the  most 
profitable  part  of  his  business.  Certain  crops  he  is 
raising  or  certain  animals  he  is  keeping  may  yield 
an  actual  loss.  He  may  be  gaining  in  some  other 
line  so  that  at  the  end  of  the  year  he  feels  that 
there  has  been  a  profit,  but  a  greater  gain  might 
have  resulted  if  he  had  discontinued  certain  activi- 
ties. The  accounts  will  also  be  a  protection  in  case 
of  dispute  or  death. 

Farm  Inventory.  No  merchant  would  feel  that 
he  knew  exactly  how  his  business  stood  unless  he 
took  an  inventory  of  his  stock  at  least  every  year ; 
the  farmer  should  feel  the  same.  A  farm  in- 
ventory includes  the  land,  stock,  machinery,  tools, 
hay,  grain,  household  goods,  accounts,  cash,  debts, 
and  all  property  belonging  to  the  farmer.  In  tak- 
ing an  inventory,  the  actual  value  of  the  different 
items  based  upon  local  prices  should  be  used. 

55 


56 


FARM  ACCOUNTS 


Study  Exercise 

63.   How  to  arrange  and  make  a  farm  inventory. 

In  arranging  an  inventory  all  the  different  items 
should  be  carefully  enumerated  with  the  estimated 
value  of  each  and  put  in  the  following  tabular  form  : 


320 
3 
2 

3 

5 

2.5 

6 

40 

4o 

200 

GOO 


acres  of  land  @  $  75  per  acre  .  . 

horses  @  ^  '^25  each 

horses  @  $175  each 

horses  @  $  150  each 

milch  cows  @  8  65  each  .... 
two-year-old  steers  @  f  25  each  . 
brood  sows  @  $25  each  .     .     .     . 

sheep  @  $7  each 

shoats  @  f  4  each 

chickens  @  65c  each 

bushels  of  corn  in  the  crib  @  60c 
Total  resources 


$  24,000.00 
675.00 
3.50.00 
450.00 
325.00 
625.00 
150.00 
280.00 
180.00 
1.30.00 
360.00 


1.  Make  out  an  inventory,  itemizing  the  differ- 
ent assets  of  your  father's  farm  or  some  other  farm 
with  which  you  are  familiar. 


Study  Lesson 

64.  How  to  start  a  farm  account  book  and  keep 
a  cash  account. 

In  starting  a  set  of  books  provide  a  ruled  blank 
book  of  reasonable  size  and  shape.  Use  the  first 
page  or  pages  for  the  inventory.  Upon  the  first 
double  pages  following  the  inventory,  write  at  the 
top  of  the  page  the  word  "receipts,"  and  on  the 


THE  CASH  ACCOUNT  57 

opposite  page  at  the  right  the  word  "expenditures." 
As  money  is  paid  out  or  received  in  cash,  enter  it 
on  the  book  by  date  and  amount. 

Keep  all  these  accounts  until  the  close  of  the 
month,  and  then  balance  the  account.  Draw  two 
lines  close  together,  leave  a  little  space,  and  then 
begin  the  new  account.  If  the  page  is  full  turn  to 
the  next  two  pages  and  write  '* receipts"  and  "ex- 
penditures "  as  before. 

In  case  there  is  a  balance  on  hand  after  closing 
the  account  of  the  previous  month,  enter  the  amount 
under  "receipts"  as  "balance  brought  forward."  If 
there  is  a  deficit,  enter  this  amount  under  "  expen- 
ditures "  as  "  deficit  brought  forward." 

Do  the  same  for  each  month;  and  at  the  close  of 
the  year  the  books  will  show,  when  the  new  in- 
ventory is  made,  whether  there  has  been  a  profit 
or  loss. 

For  all  ordinary  purposes  only  one  book  is  neces- 
sary. If  a  man  desires  to  make  allowances  for  his 
own  work  or  for  that  of  the  members  of  his 
family,  the  estimated  value  of  the  labor  should  be 
itemized  with  the  "  expenditures."  By  careful  ac- 
counting he  will  be  able  to  determine  at  the  close 
of  the  year  what  has  been  the  returns  for  their 
labor. 

1.  Suppose  on  January  1, 1914,  a  farmer  has  on 
hand  $  25  cash ;  January  3,  buys  one  ton  of  bran 
at   $24;    January   5,  sells  2  hogs  @    $  16   each; 


58 


FARM  ACCOUNTS 


January  8,  sells  30  bushels  of  corn  for  $  18 ;  Jan- 
uary 15,  pays  $22  for  labor;  January  18,  buys  10 
pigs  for  $  55 ;  January  23,  sells  475  bushels  of 
wheat  at  $  1.05  per  bushel;  January  25,  sells  7  tons 
of  hay  at  $  12  per  ton  ;  January  26,  sells  a  horse  at 
$  175.  Indicate  these  amounts  in  the  account 
book  and  then  open  up  the  books  ready  for  the 
accoimts  during  February. 


Left-Hand  Page 


1914 

fa^v.  / 

^£^aA  o-rv  kcincL 

f  25 

00 

^an.  6 

S'wo-  kocjO'  @i  •f/6  UK^k 

32 

00 

fcin.  8- 

30  {yuoA&U,  oj^  e^avn  %   60^ 

/8 

00 

fa.yi.  23 

^75  6-t(^h&U  aj  wA&at  @  ^/.Oo 

HS 

75 

fa.n.  £6 

7  txym^  of  alfaCfx  koAf  @  //2 

s^ 

00 

jam..  26 

/  koi^e^ 

/7S 

00 

^832 

75 

Right-Hand  Page 


1914 

ja/n,.  3 

/  t(yyi  of-  {^■TM.n 

f  2Jf 

00 

fan.  /5 

La^h-o-v  to  S^vayyik  W-ittla.'m.a, 

22 

00 

fa.n.  /8 

fO  aJioaX^  @  f5.50  e^oA^k 

55 

00 

fa,n.  3/ 

Bu  6-cita/yie& 

73/ 

75 

$832 

75 

In  starting  the  month  of  February  the  balance, 
or  $  731.75,  would  be  placed  on  the  page  given  to 


SPECIAL  ACCOUNTS  59 

"  receipts  "  dated  February  1  as  '^  balance  brought 
forward."  Other  items  would  then  be  entered  as 
usual  under  either  "  receipts  "  or  "  expenditures." 

Study  Lesson 

65.   How  to  keep  special  accounts. 

If  a  farmer  wishes  to  know  how  much  he  is 
making  or  losing  on  his  business  each  year,  or 
what  has  been  the  profit  or  loss  on  each  crop  or 
class  of  animals,  it  is  necessary  for  him  to  keep 
special  accounts.  These  accounts  should  cover  the 
different  crops,  the  live  stock,  labor,  personal 
accounts,  etc. 

In  keeping  a  record  of  live  stock  a  separate  ac- 
count should  be  kept  for  each  kind.  Likewise  for 
each  of  the  grain  crops,  since  on  one  crop  there 
might  be  a  gain,  while  on  another  a  loss ;  and 
hence,  if  only  one  account  is  kept,  there  might  be 
a  gain  on  all  together  but  a  loss  on  some  one  of 
them. 

An  account  of  live  stock,  fruit,  garden,  poultry, 
etc.,  may  be  kept  in  exactly  the  same  way.  The 
profit  or  loss  for  the  year,  on  everything,  will 
be  the  difference  between  the  sums  of  the  profits 
and  losses  on  the  different  items.  It  would 
be  well  for  every  farmer  to  keep  from  time  to 
time  the  special  accounts,  even  if  he  does  not  think 
it  advisable  to  keep  them  all  during  the  same 
year. 


60 


FARM  ACCOUNTS 


The  following  is  an  account  of  the  total  cost  of 
production  and  the  receipts,  on  GO  acres  of  wheat : 


1913 

E 

XPENDITUBES         RbOEIPTS 

CCt^. 

/5  S^av  ja,to-\v-VKCf  60  <x^ve^ 

f  82.80 

^€,jit. 

5 

S've/^vvyvcf  toAui;  6  cCoa^q. 

fav  ^  t&a^m^     . 

63.60 

€et. 

/ 

cf&e^d  w-k^at,  75  (y-u^&i^ 

@  9^^       .... 

67. 60 

€el. 

¥■ 

■f  cL(Xi^  cLvittiruf^  ^  cLvLtU/ 

2^.00 

1914 

/ 

<S-uttvna  CL-yvct  oJio-sJcAyyta 

60.00 

futy. 

2¥- 

S^kveAAincf  /200  {yu^k&l^ 

^8.00 

jwiy. 

27  Skie^fvUui  toM^v 

60.00 

fvoty, 

30 

fi-cxutiyva  to-  'yyucixJoet 

26.00 

fu.ttf 

SO 

^atcL  /OOO  6^^eU  @  // 

f/000.00 

^e^. 

/ 

ofolcC    /60    {ynQ.keU'    pyo 

<i.&&d  @  ff.25      .       , 

/  87.60 

c/^. 

/ 

lA^&d  ^ov  &'X^ka.'Ka&  io-v 

tto-uv,  60  (yiooAeZi/ 

60.00 

<Jnt&v&aZ    an    60    aeA^e^^ 

ta/yul  @  ^%  .      .      . 

fV-^.OO 

S'a/yceA. 

3^otat^    .       .        / 

76.00 

6^0.(^0  ^/237. 60 

B>u>-lit     .      .       . 

6(^6. 60 

66. 


Written  F*roblems 
1.    Itemize,  using  the  local  yield  and  price, 


the  cost  of  producing  50  acres  of  corn. 


PRACTICAL  EXERCISES  61 

2.  Make  up  a  similar  account  with  a  20-acre  field 
of  alfalfa. 

3.  The  following  account  was  kept  in  connection 
with  the  record  of  a  14-acre  field  of  potatoes. 
Arrange  the  items  in  the  form  shown  above.  June 
3,  160  bushels  of  seed  @  45|2^  per  bushel;  June  4, 
corrosive  sublimate,  3  ounces  @  10^  per  ounce; 
June  10,  43|-  bushels  of  seed  @  55i^  per  bushel; 
June  11,  corrosive  sublimate,  6  ounces  at  10^  per 
ounce;  July  12,  Paris  green,  6  pounds  @  22j^  per 
D<5und ;  July  15,  lead  arsenate,  160  pounds  at  9^  per 

^ pound;  use  of  land,  $5  per  acre;  man  labor,  796 
hours  @  19.02)^  per  hour;  horse  labor,  839  hours 
(p)  10.46^  per  hour;  equipment  labor,  839  hours 
@  3.5j^  per  hour ;  manure,  |-  of  the  1912  applica- 
tion, $  20 ;  manure,  all  of  the  1913  application, 
$  30  ;  sold,  Oct.  6,  226  bushels  @  60.18^  per  bushel; 
Oct.  20,  510  bushels  @  62^  per  bushel;  Nov.  1, 
241  bushels  @  $  1.083  ;  saved  for  seed,  135  bushels 
@  $  1 ;  saved  for  home  use,  16  bushels  @  60i^  per 
bushel ;  saved  f  of  the  1913  manure  and  ^q  of  the 
1912  manure.     What  were  the  profits? 

3.  Itemize  the  following  dairy  herd  account  and 
find  the  gain  or  loss:  inventory,  $1950;  feed, 
/  $1403.40;  labor,  $560;  interest  and  housing, 
$330;  incidentals,  $57;  dairy  sales,  $1998.10; 
skim  milk,  $300;  manure,  $510;  milk  for  home, 
$73;  December  31,  inventory,  $2175. 


DENOMINATE   NUMBERS* 

67.  A  denominate  number  is  a  quantity  whose 
unit  of  value  has  been  fixed  by  law  or  usage,  as  3 
feet,  4  pounds. 

A  simple  denominate  number  is  one  composed  of 
a  single  denomination,  as  5  gallons. 

A  compound  denominate  number  is  one  composed 
of  units  of  two  or  more  denominations,  as  6  bushels 
2  pecks. 

ENGLISH  UNITS   OF  MEASURE 

Linear  Measure 

68.  Linear  measure  is  used  in  measuring  lengths 
and  distances.     The  unit  of  measure  is  the  yard. 


Memorize 

THE  Table 

12  inches 

(in.) 

=  1  foot  (ft.) 

3  feet 

=  1  yard  (yd.) 

5^  yards 

=  1  rod  (rd.) 

16|-  feet 

=  1  rod 

320  rods 

=  1  mile  (mi.) 

5280  feet 

=  1  mile. 

*NoTE.  —  For  tables  of  Miscellaneous  Measures  see  Appendix  II. 

62 


SURFACES  AND  SOLIDS  63 

Surface  Measure 

69.  A  surface  has  two  dimensions,  length  and 
width.  A  plane  surface,  bounded  by  any  number 
of  lines,  is  called  a  polygon.  If  the  polygon  has 
four  sides  and  the  corners  square,  it  is  called  a 
rectangle.  The  area  of  a  rectangle  equals  the  prod- 
uct of  the  length  and  width.  Square  measure  is 
used  to  measure  areas. 


Memorize  the  Table 
144  square  inches  (sq.  in.)  =  1  square  foot  (sq.  ft.) 

9  square  feet  =  1  square  yard  (sq.  yd.) 

30|  square  yards  =  1  square  rod  (sq.  rd.) 

2721  square  feet  =1  square  rod 

160  square  rods  =  1  acre  (A.) 

640  acres  =  1  section  (sec.) 


Cubic  Measure 
70.  Cubic  measure  is  used  in  measuring  solids. 
If  the  faces  of  the  solid  are  rectangles,  the  solid  is 
called  a  rectangular  solid,  and  the  volume  is  equal 
to  the  product  of  the  length  by  the  width  by  the 
depth,  or  height. 


Memorize  the  Table 
1728  cubic  inches  (cu.  in.)  =  1  cubic  foot  (cu.  ft.) 
27  cubic  feet  =  1  cubic  yard  (cu,  yd.) 

128  cubic  feet  =  1  cord  of  wood 

24|  cubic  feet  =  1  perch  of  stone 

1  cubic  foot  of  water  weighs  62|-  pounds. 


64  DENOMINATE  NUMBERS 

Avoirdupois  Weight 
71.   Avoirdupois  weight  is  used  in  weighing  all 
ordinary  articles. 


Memorize  the  Table 
16  ounces  (oz.)  =  1  pound  (lb.) 
100  pounds  =  1  hundredweight  (cwt.) 

20  cwt.  or  2000  pounds  =  1  ton  (T.) 

2240  pounds  =  1  long  ton  (L.T.) 


The  long  ton  is  used  in  United  States  custom- 
houses in  determining  the  duty  on  merchandise 
taxed  by  the  ton.  It  is  also  used  in  wholesale 
transactions  in  coal  and  iron  at  the  mines. 

Liquid  Measure 
72.   Liquid  measure  is  used  in  measuring  the  ca- 
pacity of  tanks,  cisterns,  buckets,  etc.     The  liquid 
gallon   contains   231    cubic   inches.     A  gallon  of 
water  weighs  about  8 J  pounds. 


Memorize  the  Table 
4  gills  (gi.)  =  1  pint  (pt.) 
2  pints         =  1  quart  (qt.) 
4  quarts       =  1  gallon  (gal.) 


Dry  Measure 

73.   Dry  measure  is  used  in  measuring   grain, 

fruit,  vegetables,  etc.     The  standard  unit  is  the 

Winchester  bushel,  which  contains  2150.42  cubic 

inches,  and  is  a  cyhnder  181  inches  in   diameter 


MEASURE  OF  TIME  65 

and  8  inches  deep.     A  dry  gallon  contains  268.8 
cubic  inches. 


Memorize  the  Table 
2  pints  (pt.)  =  1  quart  (qt.) 
8  quarts         =  1  peck  (pk.) 
4  pecks  =  1  bushel  (bu.) 


Measure  of  Time 

74.  The  mean  solar  day  is  the  unit  for  measur- 
ing time,  and  is  the  interval  of  time  from  the  in- 
stant the  sun  crosses  any  meridian  until  it  crosses 
the  same  meridian  the  next  noon.  A  mean  solar 
year  equals  365  days,  5  hours,  48  minutes,  and  46 
seconds,  or  about  365J  days. 

The  Gregorian  calendar  is  now  used  by  nearly 
all  civilized  nations;  and,  according  to  the  plan  of 
this  calendar,  every  year  w^hose  date  number  is  di- 
visible by  four  is  a  leap  year,  unless  the  date  number 
ends  in  two  zeros,  in  which  case  the  date  number 
must  be  divisible  by  400  in  order  to  be  a  leap  year. 


Memorize 

THE  Table 

60  seconds  (sec.) 

=  1  minute  (min.) 

60  minutes 

=  1  hour  (hr.) 

24  hours 

=  1  day  (da.) 

7  days 

=  1  week  (wk.) 

30  days 

=  1  month  (mo.) 

12  months 

=  1  year  (yr.) 

365  days 

=  1  year 

366  days 

=  1  leap  year 

66  DENOMINATE  NUMBERS 

THE   METRIC   SYSTEM   OF  MEASURE 

75.  The  metric  system  of  measure  was  adopted 
by  France  in  1795.  The  meter  is  the  unit  of 
measure,  and  was  obtained  by  dividing  the  distance 
from  the  equator  to  the  pole  into  10,000,000  equal 
parts.  The  meter,  approximately  39.37  inches,  is 
the  unit  of  length. 


Measure 

of  Length 

Memorize 

THE  Table 

10  millimeters  (mm.) 

=  1  centimeter  (cm.) 

10  centimeters 

=  1  decimeter  (dm.) 

10  decimeters 

=  1  meter  (M.) 

10  meters 

=  1  decameter  (Dm.) 

10  decameters 

=  1  hectometer  (Hm.) 

10  hectameters 

=  1  kilometer  (Km.) 

10  kilometers 

=  1  myriameter  (Mm.) 

In  the  abbreviations  the  small  letters  are  used 
for  the  lower  denominations. 

Measure  of  Capacity 

76.  The  liter  is  the  unit  of  capacity.  It  equals 
a  cubic  decimeter,  or  1.0567  quarts  liquid  measure, 
or  .908  quart  dry  measure.  The  liter  is  used  in 
measuring  liquids  in  small  quantities,  the  decaliter 
in  measuring  large  quantities,  and  the  hectoliter  in 


MEASURE  OF  WEIGHT  67 

measuring  grain.    Four  liters  are  slightly  more  than 
a  gallon.     Thirty-five  liters  are  almost  a  bushel. 


Memorize  the  Table 

10  milliliters  (ml.) 

=  1  centiliter  (cl.) 

10  centiliters 

=  1  deciliter  (dl.) 

10  deciliters 

=  1  liter  (L.) 

10  liters 

=  1  decaliter  (Dl.) 

10  decaliters 

=  1  hectoliter  (HI.) 

.  10  hectoliters 

=  1  kiloliter  (Kl.) 

10  kiloliters 

=  1  myrialiter  (Ml.)                   . 

Measure  of  Weight 

77.  The  gram  is  the  unit  of  weight,  and  is  the 
weight  of  one  cubic  centimeter  of  distilled  water  at 
the  temperature  of  melting  ice.  The  gram  equals 
.03527  of  an  ounce  avoirdupois.  The  kilogram  is 
the  common  unit  of  weight,  and  is  equal  to  about 
2^  pounds  avoirdupois. 


Memorize  ' 

rHE  Table 

10  milligrams  (mg.) 

=  1  centigram  (eg.) 

10  centigrams 

=  1  decigram  (dg.) 

10  decigrams 

=  1  gram  (G.) 

10  grams 

=  1  decagram  (Dg.) 

10  decagrams 

=  1  hectogram  (Hg.) 

10  hectograms 

=  1  kilogram  (Kg.) 

10  kilograms 

=  1  myriagram  (Mg.) 

1000  kilograms 

=  1  tonne  (T.) 

68 


DENOMINATE  NUMBERS 


78. 

Table  of  Equivalents 

Table 

OF  Equivalents  for  Reference 

1  centimeter 

=      .3937  inch 

1  meter 

=  39.37'  inches 

1  kilometer 

=      .6214  mile 

1  foot 

=  30.48  centimeters 

1  yard 

=      .9144  meter 

1  mile 

=    1.609  kilometers 

1  gram 

=  15.43  grains  or  .0353  oz. 

1  kilogram 

=    2.204  pounds 

1  liter 

=      .9081  dry  quart  or  1 .057 

liquid  quarts 

1  dry  quart 

=    1.101  liters 

1  liquid  quart 

=      .9464  liter 

1  gallon 

=    3.785  liters 

1  bushel 

=  35.24  liters 

REDUCTION   OF  DENOMINATE  NUMBERS 

Reduction  Descending 
79.   Reduction   Descending    means    clianging   a 
denominate  number  from  a  larger  to  a  smaller  unit. 
1.    Reduce  36  rd.  4  yd.  2  ft.  to  feet. 
Process 
36  rd.  4  yd.  2  ft. 
5| 
198 
4 
202  yd. 

3 
606 
2 
608  ft,  Ans. 


Explanation :  1  rd.  =  5^  yd.,  36  rd. 
=  36  X  51  yd.  =  198  yd.  198  yd.  +  4 
yd.  =  202'  yd.  1  yd.  =  3  ft.  202  yd. 
=  202  X  3  ft.  =  606  ft.  606  ft.  +  2 
ft.  =  608  ft.  Hence  36  rd.  4  yd.  2  ft. 
=  608  ft. 


REDUCTION  69 

Written  Exercise 

80.  1.  Reduce  2  mi.  32  rd.   3  yd.  2  ft.  10  in. 

to  inches. 

2.  Reduce  18  gal.  3  qt.  1  pt.  to  pints. 

3.  How  many  inches  in  f  of  a  mile  ? 

4.  Reduce  ^  square  meter  to  square  centimeters. 

5.  How  many  grams  in  one  pound  ? 

6.  Reduce  f  kilogram  to  ounces. 

7.  Reduce  one  acre  to  square  feet. 

8.  Reduce  25  gal.  2  qt.  1  pt.  to  liters. 

Written  Problems 

81.  1.  Find  the  number  of  minutes  in  the  month 
of  January. 

2.  A  cubic  foot  of  distilled  water  weighs  about 
621  pounds.  What  is  the  weight  of  3  cu.  yd.  20 
cu.  ft.  ? 

3.  A  dairyman  delivers  120  gallons  of  milk 
daily,  |-  in  pint  bottles  and  the  rest  in  quart  bottles. 
How  many  bottles  of  each  kind  are  necessary  ? 

4.  How  many  iron  rails  each  60  feet  long  will 
be  required  to  lay  a  railroad  track  24  miles  long  ? 

5.  What  is  the  cost  per  hour  to  light  a  room 
with  54  burners  each  consuming  2|-  cu.  in.  a  second, 
the  price  of  gas  being  95)^  a  thousand  cubic  feet? 


70  DENOMINATE  NUMBERS 

Reduction  Ascending 
82.   Reduction  ascending  means  changing  a  de- 
nominate number  from  a  lower  to  a  higher  unit. 

I.  Reduce  175  pt.  to  bushels,  pecks,  and  quarts. 

Process  Explanation :    2  pt.  =  1  qt.       175 

oN-iyK  pt.  =  87  qt.  and  1  pt.     8  qt.  =  1  pk. 

8W        +  1  pt       ^^  ^**  ^  ^^  P^"  ^^^  ^  ^^'     ^  pk.  =  1 
j^nTq         _i_  7  at       ^^'     ■'"^  P^"  ~  ^  ^^'  ^^^  ^  P^' 

2  bu  +  2  pk  Therefore  :    175  pt.  =  2  bu.  2  pk. 

7  qt.  1  pt.   Ans. 

Written  Exercise 
83. 1.  Reduce  1500  pints  to  higher  units. 

2.  Reduce  1787  yards  to  miles,  rods,  and  yards. 

3.  Reduce  17,897  inches  to  higher  units. 

4.  Reduce  7862  centimeters  to  higher  units. 

5.  Reduce  107,240  oz.  to  pounds  and  tons. 

6.  Reduce  21,937  ft.  to  higher  units. 

7.  Reduce  1728  gills  to  higher  units. 

8.  Reduce  6745   minutes   to   hours,  days,  and 
months. 

9.  Reduce    94,685    seconds    to    minutes    and 
degrees.     See  Appendix. 

10.   Reduce  78,425  cu.  in.  to  cubic  feet  and  cubic 
yards. 

II.  Reduce    136,484    sq.   ft.    to   square   yards, 
square  rods,  and  acres. 


ADDITION  AND  SUBTRACTION  71 

Written  Problems 

84.  1.  A  farmer  harvested  87  bu.  3  pk.  6  qt.  of 
wheat  from  5  acres  of  land.  At  $1.15  a  bushel 
what  was  the  value  of  the  crop  per  acre  ? 

2.  If  it  takes  4  qt.  of  oats  for  one  feeding  of  a 
horse,  how  many  bushels  will  it  take  to  feed  6 
horses  a  year,  giving  them  two  feedings  a  day  ? 

3.  How  many  feet  per  second  are  equivalent  to 
40  miles  an  hour  ? 

4.  A  tank  9  by  4  by  5  feet  holds  how  many 
kilograms  of  water  ? 

5.  Find  the  value  of  a  field  440  meters  long  and 
620  meters  wide  at  $75  an  acre. 

ADDITION   AND   SUBTRACTION 

85.  1.  Add  :  8  gal.  3  qt.  1  pt.  2  gi. ;  12  gal.  2  qt. 
3  gi. ;  7  gal.  2  qt.  1  pt.  2  gi. ;  4  gal.  2  qt.  1  pt.  2  gi. 

Process  Explanation :  Write  the  numbers  to 

be  added  so  that  units  of  the  same  de- 
nomination will  be  in  the  same  column. 
Beginning  with  the  lowest  find  the 
sum  of  the  column  of  gills,  or  9  gills  = 
2  pt.  1  gi.  Write  the  1  gi.  under  the 
33  3  ^  J  proper  column  and  carry  the  2  pt.  to 
the  column  of  pints.  The  sum  of  the 
second  column  is  5  pints,  or  2  qt.  1  pt.  Bring  down  the  1  pt., 
carry  the  2  to  the  quart  column,  and  add.  The  sum  is 
found  to  be  11  qt.,  or  2  gal.  3  qt.  Write  down  the  3  qt. 
and  carry  the  2  gal.  to  the  gallons  column,  obtaining  33  for 
the  sum.     The  result  is  then :  33  gal.  3  qt.  1  pt.  1  gi.   Ans. 


gal. 

qt. 

pt. 

gi. 

8 

3 

1 

2 

12 

2 

0 

3 

7 

2 

1 

2 

4 

2 

1 

2 

72 


DENOMINATE  NUMBERS 


bu. 

pk. 

qt. 

27 

3 

2 

12 

3 

4 

2.    From  27  bu.  3  pk.  2  qt.  take  12  bu.  3  pk.  4  qt. 

Process  Explanation:    Write    the   minuend  and 

subtrahend  with  units  of  the  same  denomi- 
nation in  the  same  column.  Since  we  can- 
not subtract  4  qt.  from  2  qt.  we  take  1  pk., 
or  8  qt.,  from  the  3  pk.,  which  combined  with 
the  2  qt.  make  10  qt.     4  qt.  from  10  qt. 

leaves  6  qt.     Again,  we  cannot  take  3  pk.  from  2  pk.,  so  we 

take  1  bu.  or  4  pk.  from  the  27  bu.,  which  added  to  the  2  pk. 

make  6  pk.     3  pk.  subtracted  from  6  pk.  leaves  3  pk.     12 

bu.  from  26  bu.  leaves  14  bu. 

Hence  our  result  is :  14  bu.  3  pk.  6  qt.   Ans. 


14       3       6 


Written  Exercise 


86.  Add: 

gal.   qt.   pt.   pi. 

1.  6  3  2  3 

5  2  12 

6  113 


mi.  rd.  yd.  ft.  In. 

6  140  3  2  8 
8  143  5  2  0 

7  17  0  0  0 
0  167  3  2  9 

79  143  5  2  7 


bu. 

pk. 

qt. 

pt. 

A. 

sq.  rd. 

sq.  yd. 

sq.  ft. 

sq.  in. 

5 

3 

6 

1 

4.   9 

143 

23 

7 

126 

7 

2 

5 

1 

18 

86 

15 

7 

87 

9 

3 

3 

1 

17 

159 

27 

3 

115 

8 

3 
1 

5 

7 

1 
0 

16 

98 

17 

6 

143 

8 

5.  Add  :  10  T.  7  cwt.  55  lb. ;  17  T.  9  cwt.  85  lb.; 
19  T.  11  cwt.  60  lb. ;  13  T.  8  cwt.  18  lb. ;  and 
16  T.  17  cwt.  28  lb. 


ADDITION  AND  SUBTRACTION  73 

6.    Find  the  sum  of  f  of  a  day,  7f  hr.  9J^  min. 
53  sec.  and  7  da.  11  hr.  8  min.  16  sec. 
Subtract : 


rd. 

76 

yd. 

4 

ft. 
2 

In. 

6 

A. 
8.     19 

sq.  rd. 

143 

sq.  yd.  sq.  ft. 

25     6 

38 

5 

2 

8 

8 

103 

26     3 

9.    From  96  bu.  3  pk.  2  qt.  take  23  bu.  3  pk.  5 
qt.  1  pt. 

10.  From  125  mi.  take  |^  of  a  rod. 

11.  From  |-  of  a  rod  take  |-  of  a  yard. 

Written  Problems 

87.  1.  From  a  20-acre  field  6  acres  150  square 
rods  were  sold.  What  was  the  remainder  worth 
at  $75  an  acre? 

2.  What  is  the  distance  around  a  field  whose  sides 
are :  32  rd.  4  yd. ;  27  rd.  4  yd. ;  and  28  rd.  5  yd.  ? 

3.  A  milk  dealer  bought  9  gal.  2  qt.  1  pt.  of 
milk  from  one  man ;  7  gal.  1  qt.  from  another ; 
and  14  gal.  3  pt.  from  a  third.  What  was  the 
milk  worth  at  6  J^  a  quart  ? 

4.  Three  fields  of  alfalfa  hay  produced  14  T. 
8  cwt.  85  lb.,  18  T.  12  cwt.  60  lb.,  and  16  T.  7  cwt. 
45  lb.,  respectively.  How  much  hay  did  the  three 
fields  produce  ? 

5.  A  gardener  sold  four  loads  of  potatoes  contain- 
ing 49  bu.  18  lb.,  51  bu.  27  lb.,  48  bu.  32  lb.,  and  46 
bu.  27  lb.     What  was  their  value  at  85)^  a  bushel  ? 


gal. 

qt. 

pt. 

8 

2 

1 
9 

74  DENOMINATE  NUMBERS 

MULTIPLICATION   AND    DIVISION   OF    DENOMI- 
NATE NUMBERS 

88.  1.    Multiply  8  gal.  2  qt.  1  pt.  by  9. 

Process  Explanation :  1  pt.  x  9  =  9  pt.  or  4  qt. 

1  pt.     2  qt.  X  9  =  18  qt.     18  qt.  +  4  qt.  = 
22  qt.  or  5  gal.  2  qt.     8  gal.  x  9  =  72  gal. 
72  gal.  4-  5  gal.  =  77  gal.     The  final  result 
77      2       1      is  :  77  gal.  2  qt.  1  pt.   Ans. 

2.   Divide  17  T.  7  cwt.  15  lb.  by  5. 

Process  Explanation :  17  T.  h-  5  =  3  T.  and  a 

T.     cwt.     lb,       remainder  of  2  T.    2  T.  or  40  cwt.  +  7 

6)17      7      15      cwt.  =  47   cwt.      47  cwt.  -h  5  =  9  cwt. 

3      5      43      and  a  remainder  of  2  cwt.     2  cwt.  or 

200  lb.  +  15  lb.  =  215  lb.     215  lb.  -^  5  = 

43  lb.     Hence  our  result  is  3  T.  9  cwt.  43  lb.   Ans. 

Written  Exercise 

89.  1.    Multiply  5  gal.  3  qt.  1  pt.  3  gi.  by  23. 

2.  Multiply  6  mi.  207  rd.  4  yd.  2  ft.  8  in.  by  17. 

3.  Multiply  17  sq.  rd.  8  sq.  yd.  7  sq.  ft.  17  sq. 
in.  by  15. 

4.  Multiply  5  A.  125  sq.  rd.  29  sq.  ft.  38  sq.  in. 
by  43.5. 

5.  Divide  25  mi.  178  rd.  4  yd.  2  ft.  by  7. 

6.  Divide  10  lb.  12  oz.  by  2  lb.  7  oz. 

7.  Divide  78  da.  40  min.  40  sec.  by  1.4. 

8.  Divide  45  bu.  2  pk.  5  qt.  1  pt.  by  1  bu.  1  pk. 
1  qt.  1  pt. 


REVIEW  75 

Written  Problems 

90.  1.  A  sack  holds  2  bu.  1  pk.  4  qt.  of  wheat. 
How  much  wheat  will  45  such  sacks  hold  ? 

2.  If  land  is  valued  at  $  1200  an  acre,  what  is 
a  50  X  150  foot  lot  worth  ? 

3.  A  bin  f  full  contains  25  bu.  3  pk.  of  oats. 
What  is  its  capacity  ? 

4.  Ten  gallons  of  40  %  cream  worth  50 j^  a 
quart  are  mixed  with  10  gallons  of  milk  worth  6^ 
a  quart.  What  must  be  the  selling  price  per  quart 
of  the  mixture  in  order  not  to  lose  ? 

5.  A  ton  of  coal  contains  35  cu.  ft.  How 
many  tons  will  a  bin  12  ft.  8  in.  by  5  ft.  7  in.,  and 
4  ft.  3  in.  deep,  hold  ? 

6.  A  bushel  of  potatoes  contains  IJ  cubic  feet. 
How  many  bushels  will  a  wagon  box  hold  that  is 
12  feet  long,  3  ft.  8  in.  wide,  and  2  feet  deep  ? 

7.  A  carriage  wheel  revolves  3  times  in  going 
11  yards.  How  many  times  will  it  revolve  in 
going  |-  of  a  mile  ? 

8.  A  tract  of  land  containing  6  A.  150  sq.  rd. 
was  divided  into  31  lots  of  equal  size.  How  much 
land  did  each  contain  ? 

Written  Problems  —  Review 

91.  1.  How  many  acres  in  a  field  40  rods  by 
80  rods  ?     What  part  of  a  section  is  the  field  ? 


76  DENOMINATE  NUMBERS 

2.  How  wide  must  a  plot  of  land  be  to  contain 
an  acre,  if  it  is  160  rods  in  length  ? 

3.  A  rectangular  field  contains  35  acres.  If  it 
is  40  rods  wide,  what  is  its  length  ? 

4.  A  field  is  60  rods  by  80  rods.  How  wide  a 
strip  must  be  plowed  along  the  side  of  the  field  to 
plow  an  acre  ?     Across  the  end  ? 

5.  Approximately  300  pounds  of  water  are 
required  to  produce  one  pound  of  dry  matter  of 
corn.  How  many  gallons  would  be  required  to 
mature  a  shock  of  corn  weighing  350  pounds  ? 

6.  If  an  acre  produced  50  bushels  (72  pounds 
per  bushel)  of  corn  and  3600  pounds  of  stalks  and 
leaves,  how  many  gallons  of  water  would  be  used 
in  maturing  the  crop  ? 

7.  A  rainfall  of  one  inch  upon  an  acre  would 
weigh  how  many  pounds  ?  How  many  gallons  ? 
How  many  inches  of  rainfall  would  be  required  in 
maturing  an  acre  of  corn  of  50  bushels  ? 

8.  The  average  rainfall  for  Iowa  during  the 
year  1913  was  about  29.95  inches.  What  frac- 
tional part  of  this  would  be  required  to  yield 
60  bushels  of  corn,  and  4300  pounds  of  stalks 
and  leaves,  if  all  of  it  were  available  for  use  ? 

9.  After  a  series  of  rains  the  total  rainfall  was 
found  to  be  3  inches.  It  was  estimated  that  f  of 
the  water  ran  off  at  once,  while  the  rest  soaked 
into  the  ground  to  be  used  by  the  plants.     What 


REVIEW  77 

was  the  number  of  pounds  per  acre  left  for  the 
plants  to  use  ? 

10.  In  a  recently  plowed  field  |-  of  the  water 
soaked  into  the  ground.  How  many  pounds  per 
acre  were  taken  up  by  the  soil  ? 

11.  The  total  rainfall  at  Manhattan,  Kan.,  is 
about  30  inches.  What  does  the  water  weigh  that 
falls  on  a  square  yard  of  ground  during  the  year  ? 
How  many  gallons  ? 

12.  Plants  use  about  l  of  this  amount.  What  is 
the  weight  of  water  used  by  an  acre  of  vegetation  ? 

13.  It  requires  about  310  pounds  of  water  to 
grow  the  grass  that  will  make  one  pound  of 
timothy  hay.  How  much  water  will  be  required 
to  produce  an  acre  of  hay  yielding  2  tons  to  the 
acre  ?     How  much  rainfall  ? 

14.  A  field  of  wheat  that  yielded  315  bushels  is 
80  rods  long  by  27J  rods  wide.  What  was  the 
yield  per  acre  ? 

15.  How  many  trees  will  be  required  to  set  ten 
rows  40  rods  long  if  the  trees  are  8J  feet  apart  in 
the  rows  ?     Make  a  drawing. 

16.  If  raspberries  yield  3600  quarts  per  acre, 
how  many  quarts  should  10  rows,  60  feet  long  and 
3  feet  apart,  yield  ?     Illustrate  by  drawing. 

17.  If  10  rows  of  raspberries  are  60  feet  long  and 
the  plants  3  feet  apart  in  the  rows,  how  many 
plants  are  required  ?     Illustrate  by  drawings. 


78  DENOMINATE  NUMBERS 

18.  How  many  square  rods  of  surface  does  it 
require  for  10  rows  of  raspberries  60  feet  long  with 
the  rows  6  feet  apart  ?     Make  a  drawing. 

19.  If  raspberries  yield  3000  quarts  per  acre, 
how  many  quarts  should  be  obtained  from  the 
patch  referred  to  in  Problem  18  ? 

20.  If  berries  shrink  one  half  in  canning,  what 
is  the  cost  of  putting  up  a  bushel  crate  of  fresh  ber- 
ries when  they  are  40  J^  a  gallon  and  quart  cans  are 
90^  a  dozen  ?     What  is  the  cost  per  quart  ? 

21.  If  a  field  yields  19,440  pounds  of  wheat, 
what  is  the  yield  per  acre  if  the  field  is  64  by 
30  rods? 

22.  A  field  is  40  rods  by  20  rods.  What  will  be 
the  total  cost  to  place  a  wire  fence  around  it  at 
22^  per  rod  for  the  wire  and  17)^  each  for  the 
posts  ?     The  posts  are  to  be  one  rod  apart. 

23.  A  farmer  placed  2000  bushels  of  corn  in 
a  crib  November  15.  The  following  spring  the 
weight  showed  a  shrinkage  of  14,000  pounds.  If 
the  market  price  was  60  J^  a  bushel  at  that  time, 
how  much  did  he  gain  or  lose  by  keeping  the  corn 
until  May  1,  receiving  65^  per  bushel?  The  taxes 
on  the  com  were  $  28. 

24.  Clover  seed  of  average  quality  weighs  about 
1.5  grams  per  1000  seeds.  How  many  seeds  to  the 
pound  ? 


GRAPHS   AND   THEIR   APPLICATION 


Study  Exercise 

92.  The  graph  has  come  to  be  a  very  common 
form  of  expression,  especially  where  statistics  are 
to  be  presented.  A  much  clearer  conception  of 
magnitudes  can  often  be  obtained  by  representing 
them  by  lines,  letting  the  length  of  the  lines  bear 
direct  relations  to  the  size  of  the  numbers  to  be 
represented.  There  are  a  great  many  ways  of  rep- 
resenting data  graphically,  such  as  by  different 
lengths  of  lines,  by  pictures  of  varying  sizes,  etc. 

1.  The  picture  given  here  represents  the  effect 
of  continuous  cropping  as  against  rotation  in  the 
production  of  wheat  at  the  Kansas  State  Experi- 
ment Station. 


Compare  the  corresponding  yields 


Kotation       (1) 
Continuous  (2) 


41.16 
32.83 


44.56 
34.95 
79 


44.08 
21.57 


22.50    bu.  per  acre. 
16.39    bu.  per  acre. 


80 


GRAPHS  AND  THEIR  APPLICATION 


2.  The  amount  of  wheat  produced  by  the  five 
leading  wheat  states  in  the  United  States  may  be 
represented  as  shown  below : 

0     50  100150  200250300350400450  500550600650  700  750 


EanRRR 

J 

Korth  Dakota 

South  Dakota 

Tlllnols 

^ 

^^ 

Written  Exercise 
^    93.   1.    Represent    the    yield    of    corn    in    the 
following    states :     Illinois,    426,320,000 ;     Iowa, 
432,021,000 ;      Indiana,     174,600,000 ;      Kansas, 
174,225,000 ;  and  Nebraska^  182^616,000  bushels. 

2.  The  number  of  milcncows  in  Wisconsin  in 
'1913  was   1,007,000;   in  Missouri,   1,337,000;  in 

Kansas,  698,000 ;  in  Indiana,  634,000 ;  and  in  Illi- 
nois, 1,007,000.     Represent  as  above. 

3.  Exhibit  in  the  form  of  horizontal  parallel 
lines  the  following  facts  relative  to  Kansas  pro- 
duction values  from  1893  to  1912  in  millions  of 
bushels:  wheat,  832;  corn,  1082;  oats,  157; 
hay,  286 ;  and  live  stock  products,  1,436. 

4.  According  to  the  government  census  report, 
V  the  values  of  some  of  the  chief  mining  products  of 

the  United  States  for  1909  were  in  millions  of 
dollars :  bituminous  coal,  401 ;  anthracite  coal, 
149  ;  petroleum  and  natural  gas,  176  ;  copper,  99  ; 
iron,  107  ;  precious  metals,  88.  Represent  the 
facts  by  lines  as  above. 


SQUARED  PAPER 


81 


25 


20 


5.  The  values  of  products  of  the  leading  indus- 
tries in  the  United  States  for  1909  were  in  millions 
of  dollars :  packing,  1,371 ;  foundry  and  machine 
shop,  1,228  ;  lumber,  1,156  ;  steel,  986  ;  flour,  884  ; 
printing,  738 ;  cotton,  628.     Express  graphically. 

The  Use  of  Squared  Paper 

94.  By  means  of  squared  paper  the  results  of 
experiments  and  observations,  statistical  tables,  and 
numerical  data  of  all 
kinds  can  be  repre- 
sented by  lines  and 
curves.  A  close  study 
of  the  following  fig- 
ure, whkh  represents  '^ 
the  change  of  temper-  |  ^^ 
ature    for   a   certain  g     , 

0)   10 

period,  will   give  an  g 
idea  of  the  method  of  h     . 

5 

representation.  The 
thermometer  was  con-  d 
nected  with  an  instru- 
ment which  marked 
out  by  means  of  a  needle  every  change  of  tempera- 
ture for  every  minute  during  the  day.  The  paper 
was  arranged  on  a  rotating  cylinder  which  was  regu- 
lated by  a  clock.  By  approximating  the  time  and 
temperature  one  is  enabled  to  tell  the  temperature 
at  any  period  during  the  time. 


^"    ^ 

^            r 

7                   X 

f              ^ 

J                 s 

7                              --^ 

'^                         !S 

7                                   ^ 

r                                                 \ 

1                                                        '^ 

t 

1 

Jl 

^  ^' 

^  ^ 

^/L"^ 

7    8    9  10  11  12  1     2     3    4 

A.M.  P.M. 

Time  Line 


5    6 


82  GRAPHS  AND  THEIR  APPLICATION 

Oral  Exercise 

95.  Answer  the  following  questions  by  reference 
to  the  temperature  graph  : 

1.  What  temperature  is  recorded  at  the  begin- 
ning and  at  the  end  of  the  observations  ? 

2.  What  is  the  highest  and  what  is  the  lowest 
temperature  recorded  ? 

3.  At  what  time  was  the  highest  temperature 
recorded  ? 

4.  At  what  times  did  the  instrument  record  a  tem- 
perature of  20  degrees  ?     24  degrees  ?    15  degrees  ? 

5.  When  did  the  instrument  record  the  slowest 
changes  of  temperature  ?  the  most  sudden  ? 

6.  What  was  the  nature  of  the  change  of  tem- 
perature from  9  A.M.  until  noon  ? 

Study  the  graph  carefully  and   determine   the 
temperature  for  the  half  hour  periods. 
Written  Problems 

96.  1.    Represent  as  above  the  temperature  on 
February  24,  1914: 


/ 


6 :  00  A.M. 

4 

2; 

;  00  P.M. 

40 

7 :  00  A.M. 

6 

2 

:  30  P.M. 

40 

8 :  00  A.M. 

8 

3: 

:  00  P.M. 

38 

8 :  30  A.M. 

9 

4; 

;  00  P.M. 

26 

9 :  00  A.M. 

,10 

4 

:  30  P.M. 

24 

10 :  00  A.M. 

18 

/S: 

:  00  P.M. 

20 

10 :  30  A.M. 

22 

5 

:  30  P.M. 

15 

11 :  00  A.M. 

32 

6 

:  00  P.M. 

10 

12 :  00  M. 

35 

7 

:  00  P.M. 

4 

1 :  00  P.M. 

36 

8 

:  00  P.M. 

0 

WRITTEN  PROBLEMS  83 

2.  Represent  by  means  of  the  squared  paper  the 
following  facts  regarding  the  average  monthly 
rainfall  in  inches  at  North  Platte,  Nebr.,  for  35 
years  ending  1909  : 

Jan.  .42  May  2.86  Sept.  1.47 

Feb.  .49  June  3.41  Oct.  1.10 

Mar.  .81  July  2.90  Nov.  .46 

Apr.  2.04  Aug.  2.37  Dec.  .49 

3.  Construct  a  temperature  chart  from  the  fol- 
lowing data  regarding  the  mean  monthly  tempera- 
ture for  Ohio  from^  1888  to  1909 : 

Jan.  28.9  May  60.  Sept.  65.5 

Feb.  28.1  June  69.6  Oct.  52.5 

Mar.  38.8  July  73.1  Nov.  41.4 

Apr.  49.7  Aug.  71.3  Dec.  31.8 

4.  In  an  orchard  heating  experiment  at  the  Iowa 
Station  on  the  night  of  May  1,  1911,  the  follow- 
ing temperature  readings  were  taken  : 

Location  a.m.    2:30  8:00  3:15  8:30  4:00  4:80  5:00  6:00  7:00  8:00 

Inside  heated  area  29J      SIJ      8'2J      32      81j      32J      33       84       86       88 

Outside  heated  area  29        2Si      28       2Ti    26i      2Gi      26^      26i      84       88 

Represent  the  above  data  by  means  of  a  graph, 
thereby  visualizing  the  effect  of  the  heaters.  Use 
colored  chalk  or  different  kinds  of  broken  lines  to 
represent  the  two  sets  of  facts.  The  heating  pots 
were  lighted  between  2 :  30  and  3  :  15  a.m.,  and 
opened  wider  at  4 :  00  a.m.  The  figures  in  the 
table  are  the  averages  of  several  readings. 

5.  Show  graphically  the  rise  in  orchard  temper- 
ature due  to  the  use  of  heaters  in  accordance  with 


84  GRAPHS  AND  THEIR  APPLICATION 

the  following  tabulated  results  of  an  experiment  at 
the  Iowa  station : 

Location  a.m.    2:00  3:00  3:15  3:30  4:00  4:30  5:00  5:30  5:45  6:00 

Heated  area  —      —     29     31     35     32     32     32     37    32 

Unheated  area  31      29    29    29     29     29     30     29     29    29 

The  heaters  were  lighted  at  3 :  15  a.m.  The 
somewhat  abrupt  variations  in  the  temperature  of 
the  heated  area  are  due  to  the  partial  opening  and 
closing  of  the  covers  of  the  heaters. 

6.  The  average  values  per  acre  of  United  States 
farm  land  during  recent  decades  were  in  round 
numbers : 

1850     $14  1870     $22  1890     $26  1910     $47 

1860     $20  1880     $23  1900     $24 

Represent  the  above  data  by  means  of  a  graph. 

7.  Exhibit  by  means  of  a  coordinate  graph  the 
following  table  of  percentages  of  school  attendance 
of  the  total  population  of  the  United  States  from 
6  to  20  years  of  age : 


Age 

Peb  Cent 

Age 

Pee  Cent 

Age 

Per  Cent 

6 

52 

11 

91 

16 

51 

7 

75 

12 

90 

17 

35 

8 

83 

13 

89 

18 

23 

9 

86 

14 

81 

19 

14 

10 

90 

15 

68 

20 

8 

8.  Represent  graphically  the  following  facts  con- 
cerning the  death  rate  from  tuberculosis  in  the 
United  States  from  1900  to  1912  per  100,000  pop- 
ulation : 


WRITTEN  PROBLEMS  85 


EAR 

Deaths 

Year 

DEATU8 

Ybar 

Deatiii 

900 

202 

1904 

201 

1908 

167 

901 

197 

1905 

193 

1909 

162 

902 

185 

1906 

181 

1910 

161 

903 

188 

1907 

178 

1911 
1912 

159 
149 

9.  Construct  a  rain  chart  from  the  following 
precipitation  table  at  Hays,  Kansas,  from  1903  to 
1913: 


Year 

Uainfall  in 
Inches 

Year 

Rainfall  in 

Inches 

Year 

Rainfall  in 
Inches 

1903 

32.5 

1907 

25.4 

1911 

17.1 

1904 

15.8 

1908 

25.4 

1912 

20.2 

1905 

20.7 

1909 

28.3 

1913 

23.1 

1906 

23.1 

1910 

16.2 

10.  At  the  Wisconsin  Experiment  Station  the 
following  table  of  results  was  obtained  from  differ- 
ent groups  of  dairy  cows  for  the  year  1910.  The 
net  profits  are  found  by  deducting  the  cost  of  feed 
from  the  value  of  milk  and  butter  fat : 


oup 

Av.  Butter  Fat 
in  Pounds 

Av.  Net  Profit 
IN  Dollars 

Group 

Av.  Butter  Fat 
IN  Pounds 

Av.  Net 
Profit  in 
Dollars 

1 

674 

115 

8 

421 

63 

2 

569 

91 

9 

399 

54 

3 

529 

85 

10 

375 

46 

4 

494 

74 

11 

355 

50 

5 

472 

69 

12 

327 

45 

6 

456 

70 

13 

275 

30 

438  68 


Exhibit  these  results  graphically.  Note  relations 
between  the  two  curves  obtained  from  the  second 
and  third  columns  of  figures. 


MEASUREMENTS 
PARALLELOGRAM  AND   TRIANGLE 

97.  A  polygon  may  be  defined  as  a  plane  figure 
bounded  by  any  number  of  straight  lines.  The 
point  where  two  sides  meet  is  called  a  vertex.  The 
distance  around  a  polygon  is  called  its  perimeter. 
A  line  joining  any  two  vertices  not  adjacent  is 
called  a  diagonal  of  the  polygon. 

A  quadrilateral  is  a  polygon  having  four  sides. 

A  parallelogram  is  a  quadrilateral  whose  opposite 
sides  are  parallel. 

A  rhombus  is  a  parallelogram  having  equal  sides. 

A  rectangle  is  a  parallelogram  whose  angles  are 
right  angles. 


Parallelogram  Rectangle 

A  square  is  a  rectangle  having  equal  sides. 
A  trapezoid  is  a  quadrilateral  with  one  pair  of 
opposite  sides  parallel. 


Rhombus  Trapezoid 

86 


PARALLELOGRAM  AND  TRL\NGLE 


87 


A  triangle  is  a  polygon  having  three  sides. 

The  side  upon  which  the  figure  rests  is  called  the 
base. 

The  perpendicular  distance  from  the  base  to  the 
opposite  vertex  is  called  the  altitude. 

A  triangle  having  one  right  angle  is  called  a 
right  triangle. 


A  Triangle  Right  Triangle 

A  triangle  with  two  equal  sides  is  called  an 
isosceles  triangle. 

A  triangle  with  three  equal  sides  is  called  an 
equilateral  triangle. 


Isosceles  Triangle 


Equilateral  Triangle 


Study  Exercise 

98.  By  a  study  of  the  accompanying  figure  it 
can  be  seen  that  any  parallelo- 
gram may  be  made  into  a  rec- 
tangle having  the  same  base  and 
altitude.  Therefore,  the  area  of 
a  parallelogram  is  equal  to  the  product  of  the  base 
by  the  altitude. 


88  MEASUREMENTS 

Formula : 

Area  =  base  x  altitude. 
A  =  ba. 


The  figure  above  shows  that  the  diagonal  divides 
the  parallelogram  into  two  equal  triangles.  There- 
fore the  area  of  a  triangle  is  equal  to  one  half  the 
product  of  the  base  and  altitude. 

Formula :     Area  =  ^  base  x  altitude. 

If  the  trapezoid  ABCD  is  cut  by  EF  midway 
between  AB  and  CD,  and  the  upper  part  is  placed 
so  that  CF  will  fall  c 

upon   BF,  a   paral- 
lelogram   is   formed    V 

with  a  base  equal  in     (^ 

length  to  the  sum  of  the  upper  and  lower  bases. 
The  altitude  equals  to  one  half  the  altitude  of  the 
trapezoid ;  hence,  the  area  of  a  trapezoid  equals  one 
half  the  altitude  times  the  sum  of  the  two  bases. 

Formula :  A=^\a{h-\-  V) 

Written  Exercise 
99.   Find  the  area  of  the  following  figures : 

1.  Rectangle,  base  96  rods,  altitude  64  rods. 

2.  Rectangle,  base  84  feet,  width  45  feet. 

3.  Parallelogram,  length  73  rods,  altitude  37 
rods  4  yards. 


PARALLELOGRAM  AND  TRL4NGLE  89 

4.  Parallelogram,  length  105  feet  4  inches,  alti- 
tude 77  feet  3  inches. 

5.  Triangle,  base  56  feet,  altitude  27  feet. 

6.  Triangle,  base  37  feet,  altitude  29  feet. 

7.  Triangle,  base  89  feet  7  inches,  altitude  77 
feet  3  inches. 

8.  Trapezoid,  lower  base  58  feet,  upper  base  46 
feet,  altitude  25  feet. 

9.  Trapezoid,  lower  base  26  feet,  upper  base  16 
feet,  altitude  8  feet. 

10.    Trapezoid,  lower  base  39  feet,  upper  base  23 
feet,  altitude  15  feet. 

Written  Problems 

100.   1.    Find  the  area  of  the  surface  of  an  open 
box  which  is  6  ft.  long,  5  ft.  wide,  and  4  ft.  deep. 

2.  How  many  acres  in  a  triangular  field  whose 
base  is  480  rods  and  altitude  260  rods  ? 

3.  A  triangular  field  96  rods  long  contains  12 
acres.     Find  the  altitude. 

4.  What  will  be  the  cost  to  lay  a  six-foot  walk 
in  front  of  and  on  one  side  of  a  50  by  150  foot  lot, 
at  12  j^  a  square  foot? 

5.  How  many  bricks  8  by  4  by  2  inches  will  it 
take  to  lay  the  walk  in  Problem  4,  figuring  that  a  row 
of  bricks  be  laid  on  edge  entirely  around  the  walk  ? 


90 


MEASUREMENTS 


6.  What  does  it  cost  to  produce  a  field  of  wheat 
160  rods  by  86  rods  at  %  9.67  an  acre  ? 

7.  If  a  wheat  drill  is  8  feet  wide,  what  part  of 
an  acre  will  be  covered  in  going  across  a  field  160 
rods  long  ?  How  many  times  across  would  it  take 
to  cover  12  acres? 

8.  What  is  the  area  of  a  board  14  feet  long  and 
12  inches  wide  at  one  end  and  9  inches  wide  at  the 
other  ? 

f 


9.  Find  the  area 
of  the  following 
figures : 


2" 


627;  ,2.02 


627'  ^2.02 


CIRCLES 

101.   A  closed  curve  such  that  all  of  its  points  are 
equally  distant  from  a  point  within  is  called  a  circle. 
A  straight  line  from  the  center 
to  the  circle  is  called  a  radius. 

A  straight  line  through  the  cen- 
ter, terminated  at  each  end  by  the 
circle,  is  called  a  diameter. 

By  measuring  accurately  a  circle, 
and  then  measuring  the  diameter,  and  dividing  the 
circumference  or  distance  around  the  cii'cle  by  the 


CIRCLES  91 

diameter,  the  result  will  be  approximately  3^. 
Hence  the  circumference  of  a  circle  is  approximately 
equal  to  3^  (tt)  times  the  diameter,  or  2  times  it  times 
the  radius,     it  is  more  accurately  given  as  3.1416. 

Formula :  (7  =  2  7rr. 

1.    Example :     Find  the  circumference  of  a  circle 
whose  radius  is  18  inches. 

Process 

Circumference  =  2  pi  times  the  radius. 
C=2wr. 
Therefore,  C  =  2  x  3.1416  x  18  =  113.0976.     Ans. 

Written  Exercise 

102.   Find  the  circumference  of   the   following 
circles,  using  tt  as  3^  : 

1.  Diameter  14  inches.  5.  Diameter  4.56  feet. 

2.  Diameter  28  inches.  6.  Diameter  14.9  feet. 

3.  Diameter  47  inches.  7.  Diameter  426  feet. 

4.  Diameter  .39  inch.  8.  Diameter  115.6  feet. 

Find  the  circumference  of  the  following  circles, 
using  77  as  3.1416  : 


1.   Diameter  32  feet. 

5.   Radius  167.7. 

2.    Diameter  765  feet. 

6.   Radius  154.3. 

3.    Diameter  .76  foot. 

7.   Radius  ^  foot. 

4.    Diameter  49.52  feet.    8.    Radius  f  foot. 


92  MEASUREMENTS 

Written  Problems 

103.  1.  A  circular  piece  of  ground  33.94  rods  in 
diameter  is  bordered  by  a  running  track.  Find  the 
length  of  the  track. 

2.  Find  the  circumference  of  a  2-inch  pipe.  Of 
a  2|-inch  pipe. 

3.  Find  the  circumference  of  a  wheel  3  feet  6 
inches  in  diameter. 

4.  Find  the  diameter  of  a  circular  cistern  whose 
circumference  is  14  feet  8  inches. 

5.  Find  the  circumference  of  a  globe  whose 
radius  is  2  inches.     24  inches.     30  inches. 

6.  Find  the  diameter  of  a  circular  race  track 
whose  distance  around  is  880  rods. 

7.  Find  the  distance  around  the  earth,  if  its 
diameter  is  7918  miles. 

r    8.    The  moon's  radius  is  about  1082  miles.     Find 
its  circumference. 

Areas  of  Circles 

104.  The  method  of  finding  the  area  of  a  circle 
is  established  in  geometry  and  cannot  be  taken  up 
here. 

Rule:  The  area  of  a  circle  is  equal  to  one  half 
the  circumference  times  the  radius. 

Formixla:  S=^Cr. 


CIRCLES 


93 


Draw  a  circle  and  then  divide  the  circumference 
into  equal  parts.     Draw  the  radii,  cut  along  the 


radii  from  the  center  almost  to  the  circmn- 
ference,  and  then  spread  out  the  entire  circle 
into  two  parts.  The  area  of  the  circle  is  nearly 
equal  to  a  rectangle  whose  base  is  one  half  the 
circumference  and  whose  altitude  is  equal  to  the 
radius. 

The  circumference  is  equal  to  2  irr.  The  area  is 
equal  to  one  half  the  circumference  times  the  radius, 
or  one  half  of  2  irr  times  r  =  vr^. 

Rule:  The  area  of  a  circle  equals  tt  times  the 
radius  squared,  or  J  of  tt  times  the  square  of  the 
diameter. 


Formula : 


S=7rr^. 


Find  the  area  of  a  circle  14  feet  in  diameter. 
Fonnula :  Area  =  Pi  (tt)  times  tlie  radius  squared. 

S  =  1T1\ 

The  diameter  is  14  ;  hence  the  radius  is  7. 

Explanation :  .-.  Area  =  3.1416  x  (7)2=  152.9384  feet.  Ans. 


94  ME^SUREMENTS 

Written  Exercise 

105.  Find  the  area  of  each  of  the  following 
circles : 

1.  Circumference  34  inches. 

2.  Circumference  154  feet. 

3.  Circumference  66.4  feet. 

4.  Circumference  105.7  feet. 

5.  Diameter  18  feet. 

6.  Liameter  |  foot. 

7.  Diameter  6  feet  7  inches. 

8.  Radius  6  inches. 

9.  Radius  37.2  feet. 

10.  Radius  |  inch. 

11.  Radius  .56  foot. 

12.  Radius  7.83  yards. 

Written  Problems 

106.  1.  Find  the  area  of  the  cross  section  of  a  rod 
one  and  a  half  inches  in  diameter. 

2.  A  half  mile  circular  race  track  incloses  how 
many  acres  of  land  ? 

/^      3.    Find  the  area  of  a  ring  whose  inside  diameter 
is  8  inches,  and  whose  outside  diameter  is  10  inches. 

4.  In  a  steel  plate  3J  feet  by  2^  feet  are  bored 
28  round  holes,  each  IJ  inches  in  diameter.  Find 
the  area  of  the  steel  remaining. 


^^  SOLIDS  95 

5.  The  radii  of  two  circles  are  3  feet  and  6  feet. 
The  area  of  the  second  is  how  many  times  the  area 
of  the  first  ? 

6.  A  circular  sheet  of  steel  2  feet  4  inches  in 
diameter  increases  in  diameter  by  250"  ^^  ^^^  ^^" 
ameter  when  the  temperature  is  raised  by  a  certain 
amount.     Find  the  increase  in  the  area  of  the  sheet. 

fy'  7.    Find  the  area  of  the  largest  circle  that  can 
be  cut  from  a  piece  of  paper  8.5  inches  square. 

8.  Find  the  area  of  a  watch  crystal  1|-  inches  in 
diameter. 

SOLIDS 

107.  A  circular  cylinder  is  a  solid  Which 
has  two  equal  circles  joined  by  a  uni- 
formly curved  surface  called  the  lateral 
area. 

A  pyramid  is  a  solid  having  a 
polygon    for    a    base    and    trian- 
gles for  sides. 

A  circular  cone  is  a  solid  having  a  circle 
for  a  base  and  tapering  to  a  point. 

The  altitude  of  a  cylinder  is  the  perpen- 
dicular distance  between  the  two  bases,  and  of  a 
pyramid  or  cone  it  is  the  perpendicular  distance 
from  the  vertex  to  the  base. 

The  slant  height  of  a  pyramid  is  the  altitude  of 
any  one  of  the  triangles  forming  its  lateral  surface. 


96  MEASUREMENTS 

The  slant  height  of  a  cone  is  the  shortest  distance 
from  the  vertex  to  the  circumference  of  its  base. 

The  lateral  surface  of  a  cylinder  equals  the  prod- 
uct of  the  altitude  by  the  circumference  of  the  base. 

Formula :  S=2  irrh. 

The  volume  of  a  cylinder  is  equal  to  the  product 
of  the  height  by  the  area  of  the  base. 

Formula :  F=  trr^h. 

The  lateral  surface  of  a  pyramid  or  cone  equals  one 
half  the  perimeter  of  the  base  by  the  slant  height. 

Formula:  S=\ps. 

The  volume  of  a  pyramid  or  cone  equals  one 
third  the  area  of  the  base  by  the  altitude. 

Formula:  V=\  Bh. 

Written  Exercise 
108.    Find  the  surface  and  volume  of  the  follow- 
ing solids : 

1.  A  cylinder  with  diameter  5  feet,  height  5  feet. 

2.  A  cylinder  with  radius  7  feet,  height  7  feet. 

3.  A  cylinder  with  radius  6  feet  3  inches,  height 
25  feet. 

4.  A  pyramid  with  base  a  square  7  feet  on  a 
side,  height  9  feet,  slant  height  9.65  feet. 

5.  A  pyramid  with  base  a  square  9  feet  on  a  side, 
height  12  feet,  slant  height  12.8  feet. 


WRITTEN    PROBLEMS  97 

6.  A  pyramid  whose  base  is  an  equilateral  tri- 
angle with  sides  16  feet  and  area  110.8  sq.  ft., 
height  24  feet,  and  slant  height  24.42  feet. 

7.  A  cone  the  diameter  of  whose  base  is  6  feet, 
height  8  feet,  and  slant  height  8.54  feet. 

8.  A  cone  the  diameter  of  whose  base  is  12  feet, 
height  15  feet,  and  slant  height  16.15  feet. 

9.  A  cone  the  radius  of  whose  base  is  18  feet, 
height  24  feet,  and  slant  height  30  feet. 

Written  Problems 

109,  1.  How  many  bushels  of  potatoes  in  a 
conical  pile  8  feet  across  and  3  feet  high  if  it  re- 
quires 1^  cubic  feet  for  a  bushel  ? 

2.  How  many  bushels  of  corn  in  a  conical  pile 
15  feet  across  and  5  feet  high  if  21  cubic  feet  equals 
one  bushel  ? 

3.  How  many  square  feet  of  tin  will  it  take  to 
make  a  stovepipe  6  inches  in  diameter  and  2  feet 
8  inches  long?  Allow  one  inch  in  the  width  for 
making  the  seam. 

4.  If  one  gallon  of  paint  covers  250  square  feet, 
how  many  gallons  of  paint  will  be  required  for  a 
silo  20  feet  in  diameter  and  32  feet  in  height  ? 

5.  Find  the  capacity  in  tons  of  a  silo  20  ft.  in 
diameter  and  36  feet  high,  if  a  cubic  foot  of  silage 
weighs  40.7  pounds. 


98  MEASUREMENTS 

6.  What  must  be  the  diameter  of  a  30-foot  silo 
in  order  to  hold  enough  silage  to  feed  28  cows  40 
pounds  a  day  for  165  days,  if  the  silage  weighs  40 
pounds  per  cubic  foot  ? 

7.  The  outside  diameter  of  a  hollow  cylindrical 
cast-iron  shaft  18  ft.  long  is  21  inches,  the  inside 
diameter  is  12  inches.  Find  the  weight  if  cast  iron 
weighs  .26  pound  per  cubic  inch. 

8.  A  circular  stack  of  hay  12  feet  in  diameter 
has  perpendicular  sides  to  a  height  of  6  feet  and 
then  tapers  to  a  point,  the  entire  height  being  15 
feet.  Counting  512  cubic  feet  to  a  ton,  how  many 
tons  in  the  stack  ? 

9.  A  grain  bin  with  a  hopper  bottom  is  13  feet 
square  and  is  16  feet  deep  to  the  hopper.  The 
hopper  has  a  depth  of  5  ft.  How  many  bushels 
will  it  hold  ? 

10.  A  cylindrical  grain  bin  with  a  hopper  bottom 
is  16  feet  in  diameter  and  18  feet  deep  to  the 
hopper.  The  hopper  is  6  feet  deep.  How  many 
bushels  will  it  hold  ? 

11.  A  pump  with  a  6-inch  stroke  has  a  3-inch  cyl- 
inder.    How  much  water  will  it  deliver  per  stroke? 

12.  A  cylindrical  hot  water  storage  tank  is  guar- 
anteed to  withstand  a  pressure  of  85  pounds  per 
square  inch.  What  is  the  total  guaranteed  pres- 
sure for  the  inside  of  a  tank  that  is  5  feet  high  and 
12  inches  in  diameter  ? 


PRACTICAL   MEASUREMENTS 
PLASTERING,   PAPERING,  AND   PAINTING 

110.  Plastering  is  commonly  measured  by  the 
square  yard.  No  allowances  are  made  for  very 
small  openings;  and  usually  one  half  the  area  of 
the  doors  and  windows  is  allowed  in  estimating 
the  labor.  A  full  allowance  is  made  for  the  open- 
ings in  estimating  the  materials.  The  laths  are 
put  up  in  bundles  of  50  each,  and  from  28  to  30 
bundles  are  required  for  100  square  yards  of  sur- 
face. For  two  coats  with  brown  finish  2|-  barrels 
of  lime,  45  cubic  feet  of  sand,  4  bushels  of  hair, 
and  10  pounds  of  three-penny  nails  for  the  lathing, 
are  required. 

Wall  paper  is  usually  18  inches  wide  and  is  sold 
by  the  roll.  A  single  roll  is  8  yards  long  and  a 
double  roll  is  16  yards.  Borders  vary  in  width 
from  3  inches  upward.  In  papering  deductions  are 
not  made  for  borders,  since  no  allowances  are  made 
for  matching.  One  very  common  way  of  estimating 
the  number  of  double  rolls  required  for  a  room  is 
to  find  the  number  of  square  feet  above  the  base- 
board in  the  walls  and  ceiling,  deduct  for  openings, 
and  divide  by  70. 

Painting  is  usually  measured  by  the  square  yard, 


100  PRACTICAL  MEASUREMENTS 

and  no  allowances  are  made  for  openings  in  es- 
timating the  labor.  The  amount  of  paint  needed 
to  cover  a  surface  varies  with  the  nature  of  the 
surface ;  however,  under  ordinary  circumstances 
one  gallon  of  paint  will  cover  from  250  to  300 
square  feet  with  two  coats. 

Study  Exercise 

111.  1.  How  many  square  feet  in  the  walls  and 
ceiling  of  a  room  12  ft.  wide,  15  ft.  long,  and  9 
feet  high  if  there  are  2  doors  7  ft.  by  3  ft.  6  in., 
and  3  windows  6  ft.  by  3  ft.  ? 

Process  and  Explanation 

Area  of  walls  =  2  x  12  x  9  +  2  x  15  x  9  =  486  sq.  ft. 
Area  of  ceiling  =  12  x  15  =  180  sq.  ft. 

Total  area  666  sq.  ft. 

Openings : 

2  doors  =2x7x31  =  49  sq.  ft. 

3  windows  =  3x6x3  =  54  sq.  ft. 

Total  for  openings       103  sq.  ft. 
666   sq.  ft.  —  103  sq.  ft.  =  563  sq.  ft.  in   the   walls   and 
ceiling.     Ans. 

Written  Exercise 

112.  Determine  the  number  of  square  feet  in 
the  walls  and  ceilings  of  the  following  rooms,  if 
there  are  two  doors  7  ft.  6  in.  by  3  ft.  6  in.,  and 
3  windows  Q^  ft.  by  3  ft. : 

1.  16  ft.  wide,  20  ft.  long,  and  10  ft.  high. 

2.  13  ft.  wide,  15  ft.  long,  and  9^  ft.  high. 


PLASTERING  AND  PAINTING 


101 


3.  14  ft.  wide,  16  ft.  long,  and  9  ft.  high. 

4.  How  many  square  feet  in  the  sides  and  ends 
of  a  bam  40  ft.  wide,  60  ft.  long,  and  20  ft.  high 
with  gables  extending  16  feet  above  the  walls? 


Written  Problems 

113.  1.  What  will  it  cost  to  plaster  a  room  12' 
by  16'  by  9'  with  two  coats,  brown  finish,  at  47  <^ 
per  square  yard,  if  there  are  two  doors  and  three 
windows   in   the   room 


Bed  Room 


Closed 


k 


Hid 


Bed  Room 
ItfO'x  irt' 


.\J 


Bed  Pioom 
Il-0"xl5-6' 


N/^ 


Kitchen 
6-6"xlO-6' 


^v^ 


z. 


\ 


Rning  Room  N^ 
l£-0'x  IS^Of 


Living    Room 
H'-rf  X  eo-o" 


\. 


Pbrch 
J(J-6'  X  1+-0 


with  dimensions  7'  6'' 
by  4'  and  6'  6''  by  3'  8'' 
respectively  ? 

2.  What  will  it  cost 
to  rough  finish  two  bed- 
rooms at  34jz^  per  square 
yard  if  the  rooms  are 
12'  by  14'  and  10'  by 
12'  respectively  ?  Each 
room  is  8'  high. 

3.  What  will  it  cost 
for  the  material  to  paint 

a  five-room  cottage  24'  by  30'  if  it  is  8'  up  to  the 
plates  and  there  are  three  gables,  each  24'  wide 
and  8'  high?  Paint  is  $2.15  per  gallon,  and  one 
gallon  covers  250  square  feet  two  coats. 

4.  A    room   is    18'    square,  has   three  windows 
and  three  doors,  a  9-inch  baseboard,  and  a  9-foot 


102  PRACTICAL  MEASUREMENTS 

ceiling.     What  will  it  cost  to  paper  the  room  at 

35  ^  per  double  roll  ? 

Reference  in  the  following  problems  is  made  to 
the  cottage  shown  in  the  accompanying  diagram. 

5.  What  will  it  cost  to  lath  and  plaster  the 
two  adjoining  bedrooms  at  32  ^  per  square  yard  ? 
Height  of  room  9'  &",  doors  7'  6"  by  4',  and  win- 
dows 6'  6''  by  3'  8''. 

6.  Find  the  cost  of  hard  finishing  the  walls 
and  ceilings  of  the  living  room  and  dining  room 
at  47  ^  per  square  yard,  dimensions  of  doors  and 
windows  as  in  the  preceding  problem  and  the 
length  of  the  buffet  is  6  ft. 

7.  Find  the  cost  of  papering  the  walls  and 
ceilings  of  the  three  bedrooms  at  45  ^  per  double 
roll,  making  an  allowance  for  an  8-inch  baseboard. 

8-  Find  the  cost  of  papering  the  kitchen  with 
sanitary  wall  paper  at  32  ^  per  double  roll. 

9.  Find  the  cost  of  papering  the  two  front 
rooms  with  paper  at  40  ^  per  double  roll  for  walls 
and  25  ^  per  double  roll  for  the  ceilings,  running 
picture  moldings  at  3i^  per  foot,  baseboard  as  above. 

10.  If  one  gallon  of  paint  covers  300  square  feet 
of  surface  with  2  coats,  find  the  amount  of  paint 
required  to  give  two  coats  to  a  house  42  feet  long, 

36  feet  wide,  20  feet  high,  and  with  gables  18  feet 
high.  Find  the  cost  of  the  paint  at  $2.15  per 
gallon. 


ROOFING  103 

ROOFING 

114.  Roofing  is  usually  estimated  by  the  square, 
or  a  section  10  feet  square,  or  100  square  feet. 
Shingles  are  estimated  as  having  an  average  width 
of  4  inches.  They  are  laid  4,  41,  5,  5-|-,  and  6  inches 
to  the  weather.  Shingles  are  put  up  in  bunches  of 
250  to  the  bunch,  and  only  whole  bunches  are  sold. 

A  roof  is  said  to  be  half  pitch,  quarter  pitch, 
five  eighths  pitch,  etc.,  when  the  rise  is  |^,  J,  |,  etc., 
times  the  full  width  of  the  building. 

The  following  table  allows  for  waste  and  gives 
the  number  of  shingles  required  to  lay  a  square 
of  roofing  when  laid  at  various  distances  to  the 
weather. 


Inches 
TO  THE  Weather 

4 

NlTMBER 

TO  Cover  a  Square 

1000 

4* 
6 

900 
800 

5i 

700 

6 

650 

1.  How  many  bunches  of  shingles  laid  4^  inches 
to  the  weather  will  be  required  for  a  double  roof 
30  feet  wide  and  40  feet  long  ? 

Process  Explanation :      Each 

2  X  30  X  40      OA  side   of    the  roof   is  a 

=  z4  squares. 

100  ^  rectangle  30  by  40  ft. 

2^X900  ^         ^^^^j^^^  Hence2  x  30  x  40equals 

250  the  number  of   square 

Hence  87  bunches  will  be  needed,      feet  which  divided  by 


104  PRACTICAL  MEASUREMENTS 

100  gives  the  number  of  squares.  It  takes  900  shingles  for 
a  square,  and  for  24  squares  it  takes  24  x  900,  or  21,600. 
If  21,600  be  divided  by  250,  the  result  is  the  required  num- 
ber of  bunches. 

Written  Exercise 

115.  1.  In  the  table  above  how  many  shingles 
in  each  case  have  been  allowed  for  waste  ? 

2.  Find  the  number  of  bunches  required  for  a 
shed  roof  20  by  30  feet  if  laid  5  inches  to  the 
weather. 

3.  What  is  the  pitch  of  each  of  the  following 
roofs  ? 

(a)  Width  of  building  24  feet,  rise  8  feet. 
(6)  Width  of  building  40  feet,  rise  16  feet, 
(c)  Width  of  building  30  feet,  rise  12  feet. 

4.  What  is  the  rise  if  the  width  of  the  building 
is  40  feet  and  pitch  J  ?  i  ?  i  ?  |  ? 

Written  Problems 

•  116.  1.  How  many  bunches  of  shingles,  laid  4^ 
inches  to  the  weather,  are  required  to  cover  the 
roof  of  a  barn  60  feet  long,  with  rafters  26  feet 
long? 

2.  A  barn  is  65  feet  by  45  feet  and  is  20  feet  to 
the  eaves  with  the  roof  ^  pitch.  Find  the  cost  of 
painting  it  at  42)^  per  square  yard  for  double  coat. 

3.  The  roof  dimensions  of  a  house  are  46'  by 
18'.     The  house  has  one  porch  with  roof  dimen- 


BOARD  MEASURE 


105 


sions  20'  by  12'.     Find  the  cost  of  the  shingles  at 
$  3.25  per  M  if  laid  4"  to  the  weather. 

4.  A  conical  steeple  25  feet  in  diameter  at 
the  base  and  having  a  slant  height  40  feet  will 
require  how  many  shingles  to  cover  it  if  laid  5^ 
inches  to  the  weather  ? 

5.  The  rain  which  falls  on  a  roof  18  by  32  feet 
is  carried  to  a  cylindrical  cistern  7  feet  in  diameter. 
How  many  inches  of  rainfall  would  it  take  to  fill 
the  cistern  to  a  depth  of  6  f t.  ? 

40 


\ 

22 

/ 

Deck             j6 

/ 

115 

\ 

24 


24 


40 

6.  The  accompanying  figure  represents  the  plan 
of  a  roof.  The  deck  is  to  be  covered  with  tin. 
How  many  shingles  will  be  required  for  the  roof 
if  laid  4  inches  to  the  weather  ? 


BOARD  MEASURE 

117-  In  measuring  lumber  the  unit  is  the  board 
foot.  This  is  defined  as  a  square  foot  of  surface 
on  a  board  one  inch  thick.  Boards  less  than  one 
inch  in  thickness  are  considered  as  if  they  were  an 
inch  thick.     For  each  additional  fractional  part  of 


106       ,^         PRACTICAL  MEASUREMENTS 

an  inch  the  corresponding  fractional  part  must  be 
added.  Thus  a  board  16  feet  long,  1  foot  wide, 
and  IJ  inches  in  thickness  contains  24  board 
feet. 

Rule :  To  find  the  number  of  board  feet  multi- 
ply length  in  feet  by  the  width  times  the  thickness 
in  inches  and  divide  by  12. 

Width  X  leno-th  x  thickness 


Board  feet  = 


12 


Formula:  B.  F.=  '^- 

1.    Find  the  number  of  board  feet  in  25  scant- 
ling 2"  X  4"  by  18'  long. 

process  Explanation:     For    every 

foot    in    length     there    are 
25  X  ?^  X  18  =  300  B.  F.      2^    ^^^^^  ^^.^^   .^ 

multiplied  by  the  length  and  the  number  of  scantling  will 
give  the  total  number  of  board  feet. 


Written  Exercise 

Find  the  number  of  board  feet  in : 
118.   1.    30  boards  1"  by  12"  by  10'. 

2.  60  boards  1"  by  10''  by  16'. 

3.  40  boards  2"  by  6"  by  12'. 

4.  24  planks  11"  by  20"  by  18'. 

5.  36  planks  3"  by  9"  by  18'. 


BOARD  MEASURE  107 

Written  Problems 

119.  1.  A  house  is  40'  by  32'  by  18'.  How 
many  feet  of  siding  will  it  require,  allowing  ^  for 
lapping  ?     Find  the  cost  at  $  28  per  M. 

2.  Find  the  number  of  feet  of  lumber  required 
to  side  a  barn  60'  by  32'  by  18'  to  the  eaves,  with 
roof  at  J  pitch.     Find  the  cost  at  $  22.50  per  M. 

3.  A  yard  8  rods  by  16  rods  is  to  be  fenced 
with  4  running  boards  of  6-inch  stuff.  The  posts 
are  placed  8  feet  apart,  and  2"  x  4"  railing  pieces 
are  used  at  the  top  and  bottom.  Find  the  cost 
of  the  fence  if  the  boards  are  $  23  per  M,  scantling 
$  21.50  per  M,  and  posts  at  $  24  per  C. 

4.  Find  the  amount  of  the  following  bill  of 
lumber : 

25  scantling  2  in.  by  4  in.  by  10  ft.  @  $  22  per  M. 

20  scantling  4  in.  by  4  in.  by  12  ft.  @  $  22  per  M. 

30  scantling  2  in.  by  6  in.  by  16  ft.  @  $22  per  M. 

2200  ft.  of  ship  lap  @  $  25  per  M. 

2500  ft.  siding  @  $  26.50  per  M. 

150  bunches  of  shingles  @  $4.15  per  M. 

1650  posts  @  $  20  per  hundred. 

5.  Find  the  number  of  board  feet  in  8  planks 
2  in.  by  8  in.  by  12  ft. ;  12  planks  3  in.  by  8  in. 
by  18  ft. ;  24  planks  21  in.  by  14  in.  by  18  ft. ; 
and  18  planks  2^  in.  by  12  in.  by  18  ft.  What 
will  be  the  entire  cost  at  $  18  per  M  ? 


108 


PRACTICAL  MEASUREMENTS 


FLOORING 

120.    The   boards  for  flooring  are  tongued    and 
grooved.     On  account  of  the  tongues  and  grooves 

about  f  of  an  inch  of  the 
width  is  deducted.  A 
three-inch  board  then 
really  covers  a  strip  only 
2|-  inches  wide.  For 
flooring  from  about  2-|- 
to  5^  inches  wide,  the 
amount  added  for  match- 
ing and  waste  is  J  of  the 
total  floor  space.  For 
flooring  less  than  2^ 
inches,  ^  is  added. 
1.  How  much  flooring  will  be  required  for  a 
room  12  by  16  feet  if  2-inch  material  is  used  ? 

Explanation :    The    room   is   a   rec- 
tangle 12  by  16 ;  and  since  ^  is  to  be 


Process 

12  X  16  X  t  =  256. 


allowed  for  waste,  ^ 


^  times  the  num- 
ber of  square  feet  will  be  the  number 
of  feet  of  lumber  required. 


Written  Problems 

121.  1.  Find  the  cost  of  three-inch  flooring 
material  for  the  porch  of  the  cottage,  p.  101,  at 
$42  per  M. 

2.  Find  the  total  cost  of  3-inch  hardwood  floor- 
ing material   for  the    interior   floor  space  of   the 


CEMENT  CONSTRUCTION  109 

cottage  at  $  65  per  M.     Estimate  the  floor  space 
with  dimensions  not  given  at  300  square  feet. 

3.  How  much  3-inch  flooring  will  it  take  to  lay 
a  floor  16  feet  by  18  feet?     How  much  If-inch? 

4.  How  much  6-inch  flooring  is  required  for  a 
room  14'  6"  by  15'  10"  ? 

5.  What  will  it  cost  to  floor  a  room  12'  by  15' 
with  IJ-inch  oak  at  $  3.80  per  hundred  feet  ? 

6.  A  kitchen  floor  is  10'  8"  by  9'  3".  If  it  is 
laid  with  2-inch  hard  maple  flooring,  what  will  the 
lumber  cost  at  $  65  per  M  ? 

CEMENT  CONSTRUCTION 

122.  Concrete  is  a  mixture  of  water,  cement, 
and  an  aggregate  composed  of  sand,  gravel,  or 
broken  stone  in  certain  definite  proportions,  which 
when  allowed  to  harden  forms  an  artificial  stone. 
The  materials  are  mixed  in  some  stated  propor- 
tion ;  e.g.,  1  part  of  cement,  2  parts  of  sand,  and  4 
parts  of  gravel.  These  parts  are  always  measured 
in  volume,  and  the  proportion  is  known  as  a 
1:2:4  mixture. 

The  cement  may  be  purchased  in  sacks  weighing 
approximately  100  pounds,  or  containing  about  J 
barrel  or  about  1  cubic  foot.  The  crushed  stone, 
gravel,  and  sand  should  be  so  graded  in  size  that 
they  will  pack  together  in  such  a  way  as  not  to 
leave  any  large  openings. 


PRACTICAL  MEASUREMENTS 


VAETING   AGGaEQATB 


Uniform  Aooreoatb 


The  diagrams  above  show  the  economy  in  the 
use  of  varying  aggregate. 

The  sand  should  not  be  too  fine  and  should  be 
perfectly  clean.  In  mixing,  the  cement  should  be 
brought  into  contact  with  all  the  particles  of  the 
material  so  that  it  will  have  a  chance  to  bind  them 
all  together. 

Taylor  and  Thompson  in  a  Treatise  on  Concrete 
make  f©ur  proportions  which  differ  in  the  relative 
quantities  of  cement.  These  proportions  are  as 
follows : 

(1)  Rich  —  1 :  11 :  3  for  columns  and  structural  parts 
subjected  to  heavy  stresses. 

(2)  Standard  — 1:2:4  for  floors,  beams,  and  columns. 

(3)  Medium  —  1 :  2i  :  5  for  walls,  piers,  sidewalks,  etc. 

(4)  Lean  — 1:3:6  for  heavy  mass  work  which  is  only  in 
compression. 

For  determining  the  amount  of  material  in  a 
cubic  yard  of  concrete,  the  following  formulas, 
known  as  Fuller's  Rule,  give  fairly  good  results : 


CEMENT  CONSTRUCTION 


111 


Formulas : 


barrels  of  cement  required  for   1 
c-i-s-hg^  cubic  yard  of  concrete. 
Q_  p  ^-^    cubic  yards  of  sand  required  for 

27 '  1  cubic  yard  of  concrete. 


gravel 
cubic 


27 '   required    for    1 
yard  of  concrete. 

In  these  formulas 

c  equals  the  number  of  parts  of  cement. 

s  equals  the  number  of  parts  of  sand. 

g  equals  the  number  of  parts  of  gravel  or  broken  stone 


123. 


Written  Exercise 

1.    Using  Fuller's  Rule  fill   in  the  blanks 


below  and  thus  get  a  table  of  proportions  for  mix- 
ing cement : 


Formula 

Sacks  Cement 

Cu.  Yds.  Sand 

Cv.  Yds.  Gravel 

1  Cubic  Yd. 

1:2:4 

1:2^:5 

1:3:6 

1:4:8 

1:3:5 

1:2:3 

1:1 

Written  Problems 

124.   1.    How  many  barrels  of  cement,  and  how 
many  cubic  yards  of  sand  and  aggregate  will  be 


112  PRACTICAL  MEASUREMENTS 

needed  for  2 J  cubic  yards  of  concrete,  if  a  1  :  3  :  5 
mixture  is  used  ? 

2.  How  many  cubic  yards  of  concrete  will  it 
take  to  build  an  8-inch  cellar  wall  24  ft.  by  30  ft. 
by  71  .ft.  deep? 

3.  How  many  sacks  of  cement  will  it  take  to 
build  the  wall  referred  to  in  problem  2  ?  How 
many  cubic   yards   of   sand    and   aggregate,  if   a 

1  :  2|^ :  5  mixture  is  used  ? 

4.  How  many  cubic  yards  of  concrete  will  be 
required  to  put  in  a  4-inch  floor  in  a  cellar  24  ft. 
by  30  ft.  ?  What  will  be  the  cost  of  the  cement  at 
45  ^  per  sack  if  a  1  :  21 :  5  mixture  is  used  ? 

5.  How  many  cubic  yards  of  concrete  will  be 
required  to  make  a  watering  trough  8  ft.  by  4  ft.  by 

2  ft.  inside  dimensions,  if  the  thickness  is  4  inches  ? 

6.  How  many  sacks  of  cement  will  be  needed 
for  the  trough  if  a  1  :  2  :  4  mixture  is  used  ? 

7.  How  many  sacks  of  cement  will  be  needed  to 
build  a  walk  50  feet  long,  4^  feet  wide,  and  4 
inches  thick,  besides  a  ^inch  finishing  coat  ?  The 
main  part  of  the  walk  is  to  be  made  with  a  1 :  2| :  5 
and  the  finishing  coat  with  a  1 : 1  mixture, 

8.  If  the  volume  of  a  concrete  post  is  1.5  cubic 
feet,  how  many  sacks  of  cement  will  be  required  to 
make  100  fence  posts  with  a  1:3:6  mixture  ? 
What  will  be  the  cost  if  the  cement  is  45  i^  per  sack, 
the  sand  and  the  gravel  each  75^  per  cubic  yard  ? 


BRICKWORK  AND  STONEWORK  113 

BRICKWORK   AND    STONEWORK 

125.  A  common  brick  is  2  in.  by  4  in.  by  8  in. 
If  placed  in  a  wall,  the  side  exposed  to  the  outside, 
it  will  occupy  a  space  2  in.  by  8  in.,  or  16  square 
inches.  The  mortar  is 
usually  about  one-half 
inch  thick  between  the 
bricks ;  so  approximately 
7  bricks  are  required  to 
lay  a  wall  one  brick 
thick  for  every  square 
foot,  15  if  two,  and  22 

if  three  bricks  thick.  In  estimating  the  cost  of 
labor  no  allowances  are  made  for  openings,  but  a 
full  allowance  is  made  for  openings  in  estimating 
the  material.  A  bricklayer  will  lay  from  1800  to 
2000  bricks  per  day.  It  is  customary  to  consider 
the  outside  perimeter  of  the  walls  as  the  length  of 
the  wall  to  be  built. 

The  unit  of  measure  for  walls  built  of  stone  is 
the  perch.  A  perch  equals  24f  cubic  feet.  In 
common  practice  a  perch  is  considered  as  25  cubic 
feet.  In  excavating,  one  cubic  yard  of  earth  is 
considered  a  load. 

Study  Exercise 

126.  1.  How  many  bricks  will  be  required  for  a 
cellar  wall  18  feet  wide,  24  feet  long,  and  8  feet 
high,  three  bricks  thick  ? 


114  PRACTICAL  MEASUREMENTS 

Analysis 

The  perimeter  of  the  wall  is  2  x  18  plus  2  x  24  =  84  feet. 
84  X  8  =  672  square  feet  of  wall. 
672  X  22  bricks  =  14,784  bricks.     Atis. 

2.  How  many  perch  of  stone  will  be  required 
for  the  same  wall  ? 

Analysis 

Since  the  number  of  square  feet  in  the  wall  is  672  and  it 
is  one  foot  thick,  there  are  672  cubic  feet  in  the  wall.  One 
perch  equals  25  cubic  feet ;  hence,  672  -^  25  =  26.9,  or  about 
27  perch.     Ans. 

Written  Problems 

127.  1.  How  many  bricks  will  be  required  to 
build  a  cellar  wall  18  ft.  by  25  ft.  by  7  ft.,  two 
bricks  thick  ?     Three  bricks  thick  ? 

2.  How  many  bricks  will  be  required  to  build  a 
chimney  30  feet  high,  if  the  opening  from  top  to 
bottom  is  8  in.  by  8  in.  ? 

3.  Find  the  approximate  number  of  bricks  it 
will  take  to  wall  a  cistern  8  feet  deep  and  8  feet 
in  diameter  from  the  bottom  up  to  within  two  feet 
of  the  top.  The  wall  then  tapers  to  a  2-foot  diam- 
eter and  requires  200  bricks. 

4.  The  cellar  for  an  ordinary  eight-room  house 
will  be  28  ft.  by  30  ft.  How  many  bricks  will  it 
take  to  wall  the  cellar  if  the  walls  are  8  feet  high, 
two  bricks  thick  ? 


TEMPERATURE 


115 


5.  How  many  perch  of  stone  will  it  require  to 
build  the  same  wall  ?  What  will  be  the  difference 
in  price  if  the  bricks  are  worth  $  8  per  M  and  the 
stone  is  $  16  per  perch  ? 

6.  The  ordinary  cement  blocks  are  16  in.  by  8 
in.  by  8  in.  How  many  cement  blocks  will  it  take 
to  build  the  cellar  wall  in  Example  4  ?  What  will 
be  the  price  at  18  ^  apiece  ? 


100 


TEMPERATURE 

128.   For  measuring  temperature  two    kinds   of 
thermometers  are  most  widely  used —       ©      © 
the  Fahrenheit  for  ordinary  purposes,        "      ^ 
and  the  Centigrade  for  scientific  work. 
On  the  Fahrenheit  scale  the  32  degree 
mark  indicates  the   freezing   point  of 
water,  and  the   212   degree  mark  the 
boiling  point.     On  the  Centigrade  ther- 
mometer zero  is  the  freezing  point,  and 
100  degrees  is  the  boiling  point.     The 
scale  distance  between  these  limits  is 
spaced  equally  into  degrees.     Degrees      "^      ^ 
above  zero  are  marked  by  the  plus  sign,  and  those 
below  zero  by  the  minus  sign. 


loo- 
se- 


no 

30 


#  m 


Study  Exercise 
129.   1.    Change  60°  F.  to  C. 


116  PRACTICAL  MEASUREMENTS 

Process 

Since         180°  F.  =  100°  C.  between  boiling  and  freezing, 
l°F.  =  |o^  =  |°C. 
60°  -  32°  =  28°  above  freezing. 

28°  R  =  28  X  |°=  15|°  C.     Ans. 
To  change  Fahrenheit  reading  to  Centigrade  reading  use 
Formula:         C.°  =  |(F.°  -  32°). 

2.   Change  20°  C.  to  F. 

Process 

Since        100°  C.  =  180°  F. 
1°  C.  =  1°  F. 
20°  C.  =  20  X  f  °  =  36°  F. 
20°  C.  =  36°  F.  above  freezing. 
0°  C.  =  32°  F. 
.-.  20°  C.  =  36°  F.  +  32°  F.  =  68°  F.     Ans. 
To  change  Centigrade  reading  to  Fahrenheit  reading  use 
Formula  :        r.°  =  |°  C.  +  32°. 

Written  Exercise 

130.  1.  Change  128°  F. ;  22°  F. ;  and  68°  F.  to 
Centigrade. 

2.  Change  22°  C. ;  35°  C. ;  and  -  12°  C.  to 
Fahrenheit. 

3.  The  boihng  point  of  the  following  substances 
are :  benzine,  176°  F. ;  mercury,  676°  F. ;  ether, 
96°  F. ;  iodine,  347°  F.  Find  the  corresponding 
Centigrade  reading. 

4.  The  melting  point  of  the  following  substances 
are:    sulphur,  115°  C. ;  zinc,  420°  C. ;  aluminum, 


LONGITUDE  AND  TIME  117 

658°  C. ;  platinum,  1775°  C. ;  gold,,  1380°  C. ;  cast 
iron,  1200°  C.  Find  the  corresponding  Fahrenheit 
temperatures. 

5.  The  temperature  of  cream  for  best  results  in 
churning  is  about  65°  F.  What  should  be  the 
reading  Centigrade  ? 

6.  The  temperature  of  the  human  body  is  about 
98°  F.  ;  of  the  pigeon,  110°  F. ;  of  the  rabbit, 
103°  F.  What  are  the  corresponding  temperatures 
Centigrade  ? 

LONGITUDE   AND   TIME 

131.  For  fixing  locations  on  the  surface  of  the 
earth,  use  is  made  of  imaginary  lines,  called  merid- 
ians, running  north  and  south  from  pole  to  pole, 
and  also  of  imaginary  lines  running  east  and  west 
parallel  to  the  equator.  From  these  systems  of 
lines  two  have  been  taken,  one  from  each  set,  as 
the  axes  of  reference.  The  meridian  passing 
through  Greenwich,  England,  called  the  Prime 
Meridian,  and  the  equator  are  the  chosen  lines 
from  which  reckonings  are  made.  Distances  from 
these  axes  are  given  in  degrees. 

Longitude  is  the  distance  east  or  west  from  the 
Prime  Meridian. 

Latitude  is  the  distance  north  or  south  of  the 
equator.  For  example,  87°  37'  30''  W.  and  41°  53' 
3"  N.  fixes  the  position  of  Chicago. 


118  PRACTICAL  MEASUREMENTS 

Study  Exercise 

132.  From  the  fact  that  the  earth  rotates  upon 
its  axis  once  in  24  hours,  any  point  on  its  surface 
passes  in  that  time  through  360  degrees. 

By  comparing  the  number  of  degrees  passed 
through  with  the  time  it  takes  to  pass,  a  conven- 
ient table  may  be  developed.     It  follows: 


360°  are  equivalent  to  24  hours  of  time. 
15°  are  equivalent  to  1  hour  of  time. 
1°  is  equivalent  to  4  minutes  of  time. 
1'  is  equivalent  to  4  seconds  of  time. 


Since  24  hours  of  time  corresponds  to  360  degrees 
of  longitude,  the  following  table  results : 


24  hours  are  equivalent  to  360°. 
1  hour  is  equivalent  to  15°. 
1  minute  is  equivalent  to  15'. 
1  second  is  equivalent  to  15". 


1.  The  difference  of  longitude  between  Wash- 
ington and  San  Francisco  is  45°  2V  15".  What  is 
the  difference  in  time  ? 

Process  Explanation:      Since     15°    are 

15)45°    21'     15"  equivalent   to   one   hour  of  time, 

"3°       V    25"     Ans.    ^5°  21'  15"  will  be   equivalent  to 

as  many  hours  as  15  is  contained 

times   in   it.     The   problem   then   is   a  simple   one  in  the 

division  of  Denominate  Numbers. 


LONGITUDE  AND  TIME  119 

2.  The  difference  of  time  between  Greenwich, 
Eng-land,  and  Chicao'o  is  5  hrs.  42  min.  30  sec. 
What  is  the  difference  in  longitude  ? 

Process  Explanation:  Since   1  hr.  is 

5  hr.     42  min.     30  sec.  equivalent  to  15°  of  longitude, 

15  1   min.  equivalent  to   15',  and 

87°       SV  30"     Ans.   ^  ^^c.  equivalent  to  15",  5  hr. 

42  min.  30  sec.  is  equivalent  to 
15  times  aS'  much,  or  87°  37'  30". 

Written  Exercise 
133.    Find  the  difference  in  time  between: 

1.  Denver,  105°  4'  W.  and  Vicksburg,  90°  54' 
W. 

2.  Constantinople,  28°  59'  E.  and  New  York, 
74°  0'  3"  W. 

3.  St.  Louis,  90°  14'  W.  and  Paris  2°  20'  22"  E. 

4.  Portland,  Oregon,  122°  27'  30"  W.  and  Pe- 
king, 116° 27' 30"  E. 

The  difference  of  time  between  Greenwich  and 
the  following  places  is  given.  Find  their  longi- 
tude. 

5.  Liverpool,  12  min.  17.3  sec.  W. 

6.  St.  Louis,  6  hr.  49  sec.  W. 

7.  Hong  Kong,  7  hr.  36  min.  41.6  sec.  E. 

8.  Denver,  6  hr.  59  min.  47.6  sec.  W. 

9.  Find  the  difference  in  longitude  between 
Denver  and  Hong  Kong. 


120  PRACTICAL  MEASUREMENTS 

Written  Problems 

134.  1.  The  longitude  of  New  Orleans  is  90°  5' 
W.  and  that  of  Constantinople  is  28°  59'  15''  E. 
What  is  their  difference  in  local  time  ?  When  it 
is  3  P.M.  in  Constantinople  what  is  the  time  at 
New  Orleans  ? 

2.  A  vessel  at  54°  17'  30"  W.  sent  a  wireless 
message  to  one  at  61°  24'  50"  W.  at  10  a.m.  If 
transmitted  without  loss  of  time,  when  was  the 
message  received  ? 

3.  The  longitudes  of  Washington  and  San  Fran- 
cisco are  77°  2'  48"  W.  and  122°  25'  W.  respec- 
tively. When  it  is  noon  at  San  Francisco,  what 
is  the  time  at  Washington  ?  When  it  is  2  p.m. 
at  Washington,  what  is  the  time  at  San  Francisco  ? 

4.  If  a  telegram  is  sent  at  11 :  30  A.M.  from  Kan- 
sas City  in  longitude  94°  37'  40"  W.  to  Boston  in 
longitude  71°  3'  51"  W.,  allowing  20  minutes  of 
time  for  transmission,  when  will  it  reach  its  des- 
tination ? 

5.  A  cablegram,  sent  from  New  York  in  longi- 
tude 74°  0'  3"  W.,  was  received  in  Paris  in  longi- 
tude 2°  20'  221"  E.  at  1 :  30  p.m.  after  a  delay  of 
25  minutes  in  transmission.  When  was  it  sent 
from  New  York  ? 

6.  The  difference  in  time  between  two  cities  is 
1  hour,  37  minutes,  and  20  seconds.  What  is  the 
difference  in  longitude? 


STANDARD  TIME  121 

7.  .At  8:40  A.M.  a  ship  in  longitude  17°  20'  W. 
sends  a  wireless  message  whicli  is  received  by  an- 
other ship  at  8 :  45  a.m.  Find  the  longitude  of  the 
second  ship. 

8.  A  man  arriving  in  New  York  found  that  his 
watch,  set  by  local  time  at  his  starting  point,  was 
1  hour  and  26  minutes  slower  than  New  York 
time.     From  what  longitude  did  he  come  ? 

STANDARD   TIME 

135.  On  account  of  the  inconvenience  of  reckon- 
ing the  time  of  a  place  strictly  in  accordance  with 
its  meridian,  most  countries  have  adopted  a  sys- 
tem of  standard  time.  In  the  United  States  four 
time  belts,  each  15  degrees  apart,  have  been  estab- 
lished. All  points  lying  in  the  same  belt  use  ex- 
actly the  same  time,  and  the  difference  in  time 
between  places  located  in  different  belts  is  an  inte- 
gral number  of  hours.  These  belts,  or  sections,  are 
known  as  Eastern,  Central,  Mountain,  and  Pacific; 
the  central  meridian  of  each  section  being  75°,  90°, 
105°,  and  120°.  By  this  plan  when  it  is  noon  in 
Washington,  it  is  11  a.m.  in  Chicago,  10  a.m.  in 
Denver,  and  9  a.m.  in  San  Francisco. 

While  the  time  meridians  are  exactly  15°  apart, 
the  belts  using  the  several  meridian  times  vary  to 
suit  the  convenience  of  the  railroads.  They  prefer 
that  the  changes  be  made  at  some  city  on. the  road, 
and  this  leads  to  the  irregularities  in  division  lines. 


122 


PRACTICAL  MEASUREMENTS 


Standard  Time  Map  of  the  United  States. 


Oral  Exercise 

136.   What   is  the  difference  in   standard   time 
between : 

1.  Boston  and  New  Orleans  ? 

2.  Washington  and  Kansas  City? 

3.  Chicago  and  Salt  Lake  City  ? 

4.  Cincinnati  and  San  Francisco  ? 

5.  At  what  city  in  the  United  States  near  the 
105th  meridian  is  there  no  mountain  time  ? 

6.  What    is    the   difference    between    Standard 
Time  and  Sun  Time  at  El  Paso,  Texas  ? 

7.  At  San  Francisco  ? 

8.  When  it  is  noon  in  Washington  by  sun  time, 
what  is  the  correct  standard  time? 


GOVERNMENT  LAND  MEASURE 


123 


GOVERNMENT  LAND   MEASURE 

137.  Most  of  the  public  lands  of  the  United  States 
are  surveyed  by  selecting  a  north-and-south  line 
called  the  principal  meridian,  and  an  east-and-west 
line  called  the  base  line.  On  each  side  of  the 
principal  meridian  and  at  distances  of  six  miles 
are  north-and-south  lines  called  range  lines,  which 
divide  the  land  into  strips  six  miles  wide  called 
ranges. 

By  east-and-west  lines  parallel  to  the  base  line 

the     ranges    are    divided 

into  townships    six  miles 

square.      A    township    is 

designated   by   giving  its 

number  and  direction  from 

the  base  line,  the  number 

and  position  of  its  range, 

and   the   number    of    the 

principal   meridian.     Thus :    township    (A)    in   the 

figure  is  Township  4  north,  Range  3  east  of  the 

principal  meridian. 

The  townships  are  divided 
into  36  sections  numbered  as 
shown  in  the  figure.  The  sec- 
tions are  divided  into  halves 
and  quarters ;  the  quarters 
into  halves  and  quarters ;  and 
so  on. 


A 


6 

5 

4 

3 

2 

1 

7 

8 

9 

10 

11 

12 

18 

17 

16 

15 

14 

13 

19 

20 

21 

22 

23 

24 

30 

29 

28 

27 

26 

25 

31 

32 

33 

34 

35 

36 

124 


PRACTICAL    MEASUREMENTS 


(b) 

(a) 

(c) 

d 

Note  the  description  of  the  following  tracts: 
{a)  E.  i  Sec.  25,  T.  4  N.  3  E. 
(6)  N.  i  N.  W.  1  Sec.    25,   T. 
4  N.  3  E. 

(c)  N.  W.  1  S.  W.  1  Sec.  25,  etc. 

(d)  W.  J  S.  W.  i  S.  W.  1  Sec. 
25,  etc. 

Written  Exercise 

138.  Draw  a  three-inch  square  representing  a 
section,  marking  in  it  the  following  tracts,  and  tell 
how  many  acres  each  contains. 

1.  The  N.  W.  i  of  the  N.  W.  J. 

2.  The  S.  1  of  the  N.  E.  J. 

3.  The  N.  i  of  the  N.  E.  J  of  the  S.  W.  i 

4.  The  S.  W.  i  of  the  S.  E.  J  of  the  N.  W.  J  of 
the  S.  E.  1 

5.  The  S.  1  of  the  N.  W.  i  of  the  S.  E.  J. 

6.  The  S.  1  of  the  S.  E.  i  of  the  N.  E.  i  of  the 
S.  E.  i. 


REVIEW   PROBLEMS 

• 

139.   1.    There  are  11  trees  a  rod  apart  along  the 

end  of  a  field,  17  along  the  side.     How  many  acres 
in  the  field  ?     Illustrate  by  drawing. 

2.  Abraham    Lincoln    was    born   February   12,      /^ 
1809,  and  died  April  14,  1865.     How  old  was  he 
when  he  died  ? 

3.  How  many  days  from  March  15  to  Sep- 
tember 30  ? 

4.  A  boy  can  dig  18  bushels  of  potatoes  in  a  day 

and  he  can  pick  up  45  bushels  in  a  day.     How    ,    ^ 
many  bushels  can  he  dig  and  pick  up  in  three 
days  ? 

5.  A  drover  bought  247  sheep  at  S  5  each ;  it 
cost  him  $  150  to  get  them  to  market ;  and  8 
sheep  died  on  the  way.  After  selling  the  remain- 
der for  $  6.75  per  head,  how  much  did  he  gain  ? 

6.  Which  is  more  economical  to  buy,  a  farm 
wagon  for  $  52  that  will  last  8  years,  or  a  $  68 
wagon  that  will  last  11  years  ? 

7.  Allowing  for  \\  inches  overlap,  how  much 
sheet  metal  is  required  for  the  lateral  surface  of  a 
hollow  cylinder  of  14  feet  length  and  3J  in.  radius 
of  base  ? 

126 


126  REVIEW 

8.  The  weight  of  an  iron  bar  2  feet  long,  3 
inches  wide,  and  1  inch  thick  is  20  pounds.  What 
is  the  weight  of  a  bar  7^  feet  long,  4|-  inches  wide, 
and  3 J  inches  thick  ? 

9.  A  man's  assets  are  $3000,  his  liabilities 
$  4000.     How  much  can  he  pay  on  the  dollar  ? 

10.  A  bankrupt  pays  37 J^  on  the  dollar.  How 
much  will  be  lost  by  a  creditor  whose  bill  is  $  750  ? 

11.  What  will  it  cost  for  the  material  for  a  fence 
around  a  square  farm  containing  160  acres,  if  the 
fence  costs  36^  per  rod  for  woven  wire,  the  posts 
18^  apiece  put  in  a  rod  apart,  and  a  barb  wire 
placed  along  the  top  of  the  fence  requiring  480 
pounds  at  $2.75  per  hundred? 

12.  A  farm  hand  is   hired   on    April  3  for    ^-Ly 
months.     When  will  his  time  expire  ?  '^ 

13.  A  man  hauled  139  loads  of  gravel  for  a  road 
at  $  1.35  per  load.  He  paid  a  boy  15^  a  load  for 
helping  him  with  91  loads.  If  it  took  58  days  to 
do  the  work,  how  much  did  he  average  per  day  ? 

14.  What  will  7260  pounds  of  wheat  bring  at 
$  1.08  per  bushel  ? 

15.  A  farmer  takes  six  loads  of  hay  to  market.  \/ 
They   weigh   2167,  2398,  2257,  2156,  2566,  and  ^ 
2750  pounds.     What  did  he  receive  at  $  18  per  ton  ? 

16.  A  farmer's  wife  sold  a  grocer  18  dozen  eggs 
at  23^  per  dozen  and  17  pounds  of  butter  at  24^ 


PROBLEMS  127 

per  pound.  She  received  in  payment  14  pounds  of 
sugar  at  6|^  per  pound,  3  pounds  of  coffee  at  37,^ 
per  pound,  and  cash  for  the  rest.  How  much 
money  did  she  receive  ? 

17.  What  is  the  value  of  6950  pounds  of  hay  at 
$16.50  per  ton? 

18.  With  corn  at  57^  per  bushel  (70  lb.),  what 
is  it  per  cwt.  ? 

19.  How  many  acres,  in  a  farm  one  mile  long 
and  228  rods  wide  ? 

20.  A  ton  of  coal  lasts  a  family  14  days  on  the 
average.  What  will  their  coal  cost  from  October 
1  to  April  1  at  $  6.25  per  ton  ? 

21.  If  1000  laths  cover  70  square  yards  of  sur- 
face and  11  pounds  of  lath  nails  are  required  to  put 
them  on,  what  will  it  cost  to  lath  the  walls  and 
ceiling  of  a  community  building  48  ft.  by  36  ft.  by 
18  ft.  high  at  $  2  per  M  for  the  lath,  6|^  per  pound 
for  the  nails,  and  3^^  per  square  yard  for  the  labor  ? 

22.  How  many  cubic  feet  of  earth  must  be  re- 
moved in  digging  a  cistern  8  feet  in  diameter  and 
14  feet  deep  ? 

23.  How  many  bushels  of  wheat  in  a  bin  12  ft. 

by  9  ft.  by  6  ft.  ? 

24.  If  a  binder  cuts  a  swath  8  feet  wide,  how 
many  acres  will  be  cut  over  by  10  swaths  around 
a  field  80  rods  by  40  rods  ? 


128  REVIEW 

25.  What  will  it  cost  to  shingle  a  barn,  each 
side  of  the  roof  of  which  is  70  ft.  by  30  ft.?  The 
shingles  are  laid  4^  inches  to  the  weather,  cost 
$1.25  per  bunch;  and  the  labor  for  putting  them 
on  is  $  1.15  per  square. 

26.  If  1000  shingles  are  required  for  a  square  of 
roofing  when  laid  4  inches  to  the  weather,  how  many 
will  be  required  for  a  square  of  roofing  if  laid  5 
inches  to  the  weather?  When  laid  4^  inches  to 
the  weather  ?     When  laid  S  J  inches  to  the  weather  ? 

27.  Find  the  cost  of  digging  a  drain  48  rods  long, 
3  feet  deep,  S^  feet  wide  at  the  top,  and  2J  feet 
wide  at  the  bottom,  at  7i^  per  cubic  yard. 

28.  Which  will  carry  the  greater  amount  of 
water,  two  3-inch  tile  or  one  4-inch  ? 

29.  How  many  cubic  yards  of  concrete  are  re- 
quired to  make  a  semicircular  walk,  4  feet  6  inches 
wide,  48  feet  long  on  the  longer  side,  and  4  inches 
thick  ? 

30.  What  will  it  cost  to  paint  a  land  roller,  at 
27^  per  square  yard,  if  it  is  3|-  feet  in  diameter  and 
14  feet  long  ? 

31.  What  will  it  cost  to  build  the  foundation 
wall  for  a  house  28  ft.  by  36  ft.,  if  a  cellar  is  under 
the  entire  house  and  the  wall  is  7^  feet  high  and  9 
inches  thick  ?  A  1  :  3  :  6  cement  mixture  is  used 
with  the  cement  costing  45^  per  sack,  and  the 
other  material  75j^  per  square  yard. 


PROBLEMS  129 

32.  A  field  in  the  shape  of  a  trapezoid  has  one 
of  the  parallel  sides  |-  of  a  mile  long,  the  other  ^ 
jnile  long.  It  is  60  rods  wide.  How  many  acres 
in  the  field  ? 

33.  A  silo  with  staves  2  inches  thick  is  12  feet 
in  diameter,  inside  measurements,  and  30  feet  high. 
What  will  it  cost  to  creosote  the  inside  and  outside 
at  2  ^  per  square  yard  for  labor  ? 

34.  A  farmer  builds  a  barn  80  by  36  feet.  It  is 
32  feet  to  the  eaves  and  16  feet  more  to  the  comb. 
How  many  board  feet  are  needed  for  the  sides  and 
ends  ?  The  roof  is  25  by  84  feet  on  each  side. 
How  many  shingles  will  be  needed  if  they  are  laid 
4  inches  to  the  weather  ? 

35.  What  fractional  part  of  a  mile  is  2  yd.  1  ft. 
4  in.? 

36.  A  box  car  is  36  feet  long,  8  feet  wide,  and  7^ 
feet  high.  If  there  are  66,000  pounds  of  wheat  in 
the  car,  how  deep  is  the  wheat  ? 

37.  Find  the  weight  of  the  wheat  that  will  fill  a 
bin  8  ft.  by  6  ft.  by  5  ft. 

38.  What  is  the  cost  to  dig  and  wall  a  cellar  36 
ft.  by  32  ft.,  the  excavation  to  be  6  feet  deep 
and  the  wall  to  extend  2  feet  above  the  ground  ? 
The  wall  is  to  be  18  inches  thick  and  the  stone  and 
mason  work  costs  $  3.60  per  perch,  and  the  excavat- 
ing 60^  per  cubic  yard. 


130  REVIEW 

39.  If  the  wall  in  problem  38  is  three  bricks 
thick,  what  would  be  the  cost  at  $  8.50  per  M  ? 

40.  How  many  cubic  feet  are  there  in  a  stick  of- 
timber  32  feet  long,  9  inches  thick,  12  inches  wide 
at  one  end  and  7  inches  wide  at  the  other  ? 

41.  What  are  the  contents  of  a  mow  of  alfalfa 
hay  44  feet  long  by  24  feet  wide,  and  16  feet  deep, 
allowing  512  cubic  feet  for  a  ton  ? 

42.  A  man  bought  33  acres  of  land  at  $  225  per 
acre.  He  laid  it  out  in  lots  4  rods  by  10  rods  and 
sold  them  at  $  100  apiece.  How  much  did  he 
gain  by  the  transaction  ? 

43.  What  fractional  part  of  a  bushel  is  J  of  a  quart  ? 

44.  Find  the  cost  of  a  load  of  hay  weighing 
2863  pounds  at  $  9.50  per  ton. 

45.  A  man  will  dig  and  load  into  a  wagon  or 
wheelbarrow  12  cubic  yards  of  earth  in  9  hours. 
If  his  time  is  worth  25^  per  hour,  what  will  it  cost 
to  dig  a  cellar  24  ft.  by  32  ft.  by  7  ft.  ? 

46.  A  set  of  boilers  at  the  Kansas  State  Agri- 
cultural College  requires  about  600  gallons  of  water 
per  hour.  Compute  the  size  of  a  feed  water  pipe 
required  to  carry  the  water  if  the  average  velocity 
of  the  water  in  the  pipe  is  245  feet  per  minute 
(use  7r=3i). 

47.  A  steam  pump  delivers  2.35  gallons  of  water 
per  stroke  and  runs  48  strokes  per  minute.  How 
many  gallons  will  it  deliver  in  an  hour? 


PERCENTAGE 

Study  Exercise 

140.  We  have  seen  in  the  study  of  common 
fractions  and  decimals  that  the  decimal  has  many 
advantages  in  ease  of  operations  over  the  common 
fraction.  Percentage  is  very  closely  related  to  the 
decimal  fraction,  and  in  fact  may  be  considered  as  a 
development  of  the  decimal  especially  adapted  to 
business  and  to  comparisons  of  data  in  the  scientific 
world.  Instead  of  using  all  of  the  denominations 
that  are  used  in  decimals,  only  hundredths  is  used; 
hence,  percentage  is  not  a  new  subject  but  a  further 
development  of  decimals  in  which  hundredths  alone 
is  considered.     Per  cent  means  by  the  hundredths. 

An  example  will  make  the  meaning  clear. 

Example  :  A  careful  examination  of  one  pound 
of  alfalfa  seed  showed  that  J  of  a  pound  was  weed 
seed,  ^Q  of  a  pound  dirt,  and  the  rest  good  seed. 
How  many  hundredths,  or  how  many  per  cent,  of 
each  was  found  ? 

We  see  at  once  that  J  of  the  pound  was  weed 
seed,  -^  was  dirt,  and  ^  was  good  seed.  The 
fractions  J,  ■^,  -l|-  cannot  easily  be  compared  un- 
less they  are  reduced  to  the  same  denominator. 
This  comparison  can  more  easily  be  made  if  100  is 

X81 


132  PERCENTAGE 

used ;  i.e.  if  the  pound  is  considered  as  being  com- 
posed of  100  parts.  Hence,  the  amount  of  weed 
seed  may  be  represented  by  J^,  ^j^,  .25,  or  25  % ; 
the  amount  of  dirt  by  -^j  ^^^,  .10,  or  10  % ;  and 
the  amount  of  real  seed  by  J^,  j^,  .65,  or  65  %. 

Oral  Exercise 

141.  Express  the  following  per  cents  as  decimals, 
and  as  common  fractions  in  their  lowest  terms  : 

1.  3%.  7.  .4%.  13.  .35%.  19.  1%. 

2.  15%.  8.  62%.  14.  9.05%.  20.  1%. 

3.  6%.  9.  .1%.  15.  175.  21.  .003%. 

4.  65%.  10.  871%.  16.  6f %.  22.  581%. 

5.  41%.  11.  125%.  17.  .007%.  23.  66|%. 

6.  37%.        12.     3.5%.  18.     1%.  24.     6|%. 

Study  Exercise 

142.  The  number  of  which  a  certain  per  cent,  or 
hundredths,  is  to  be  taken  is  called  the  base. 

The  result  obtained  by  taking  a  certain  per  cent 
of  a  number  is  called  the  percentage. 

The  number  indicating  the  number  of  hundredths 
of  the  base  to  be  taken  is  called  the  rate. 

The  amount  is  the  base  plus  the  percentage. 
The  difference  is  the  base  less  the  percentage. 

Three  cases  of  problems  occur  in  percentage. 

Case  I.  Problems  in  which  the  base  and  rate  are 
given,  to  find  the  percentage. 


CASE  I  133 

Case  II.  Those  with  the  base  and  percentage 
given,  to  find  the  rate. 

Case  III.  Those  with  the  rate  and  percentage 
given,  to  find  the  base. 

Study  Exercise.    Case  I 

143.  Given  the  base  and  rate,  to  find  the  per- 
centage. The  percentage  equals  the  base  times  the 
rate  (expressed  as  hundredths). 

Formula  for  Case  I :  F=hxr. 

1.  Find  23  %  of  576  pounds. 

Process 

Explanation:       Apply     tlie     formula 

P=z  b  X  r.     576  pounds  is  the  base  and 

23  %    is   the    rate.     Since    23  %    of    a 

1^  28  number  is  .23  of  it,  23  %  of  576  pounds 

^^^2  =  .23  X  576  pounds  =  132.48  pounds. 

132.48  lb.     Ans. 

Oral  Exercise 

144.  1.  Find  2,  5,  8,  12,  20,  40,  50,  and  60  per 
cent  of  $  120. 

2.  Find  20  %  of  8,  12,  20,  40,  56,  80, 100,  120. 

3.  Find  1  %  and  then  i%  of  110,  120,  200,  250, 
90,  8,  4,  and! 

4.  What  is  8.31%  of  $25?  of  $72?  of  $84? 

5.  What  is  75%  of  $40?  of  $56?  of  $64? 

6.  What  is  125%  of  60  bu.?  150%  of  75  bu.? 

7.  What  is  371%  of  80?  621%  of  32?  166|% 
of  52  ? 


576  lb. 
.23 


134  PERCENTAGE 

Written  Exercise 

145.  1.  What  is  7%  of  $12.50?  $25.85? 
$65.70?  and  $254.75? 

2.  What  is  24  %  of  a  section  of  land  ? 

3.  What  is  i%  of  6278  pounds  of  milk  ? 

4.  Find  11%  of  $6754.25. 

5.  Find  I  %  of  $5943. 

6.  What  is  127%  of  $6457? 

7.  What  is  133-1%  of  6498  bushels? 

8.  What  is  .24%  of  7842.3  pounds  of  milk? 

Written  Problems      ^^y 

146.  1.  If  10  %  of  the  weight  of  wheat  is  water 
and  the  rest  dry  matter,  how  much  water  and  how 
much  dry  matter  in  30  bushels  of  wheat  ? 

2.  If  a  ton  of  coal  has  12.19  %  moisture  and  if 
6.74  %  of  the  dry  coal  is  ash,  how  many  pounds 
of  ash  does  the  ton  contain? 

3.  If  cottonseed  meal  contains  42  %  protein, 
8.67  %  fat,  and  6.32  %  fiber,  how  many  pounds  of 
each  ingredient  are  there  in  a  ton  ? 

4.  A  certain  poultry  mash  and  meal  contains 
22.94  %  protein,  5.22  %  fat,  and  5.40  %  fiber.  Find 
the  amount  of  each  in  500  pounds. 

5.  If  a  dozen  eggs  weigh  22  ounces  and  contain 
13.4  %  protein  and  10.5  %  fat,  how  many  ounces 
of  protein  and  fat  in  10  dozen  eggs  ? 


CASE  II  135 

6.  If  sirloin  steak  contains  18.9  %  protein  and 
18.5  %  fat,  how  many  ounces  of  protein  and  fat  in 
10  pounds  of  steak? 

7.  If  a  man  eats  2  eggs  and  3  ounces  of  steak, 
how  many  ounces  of  protein  and  fat  does  he  eat? 

8.  An  egg  weighs  on  the  average  1.88  ounces, 
of  which  56.96%  is  white,  33.18%  yolk,  and  the 
rest  water.  What  is  the  weight  of  each  of  the  con- 
stituents of  an  egg? 

9.  To  secure  a  yield  of  corn  of  60  bushels  per 
acre  about  30,000  pounds  of  green  corn  must  be 
produced.  It  is  estimated  that  60,000  pounds  of 
water  are  required  for  every  1000  pounds  of  green 
corn.  How  many  inches  of  rainfall  are  required  if 
all  the  water  is  available?  If  only  about  50% 
of  the  rainfall  is  available  for  the  use  of  the  crop, 
what  would  be  the  smallest  possible  rainfall  neces- 
sary to  produce  60  bushels  of  corn  per  acre  ? 

Study  Exercise.     Case  II 
147.   Base   and   percentage    given,    to    find    the 
rate.     To  find  the  rate,  divide  the  percentage  by 
the  base.     The  result  of  division  will  be  a  decimal, 
and  this  may  then  be  expressed  as  per  cent. 

The  formula  for  Case  II  is  i?=  ^• 

0 

1.  A  farmer  raised  475  bushels  of  wheat,  of 
which  he  sold  228  bu.  What  per  cent  of  the 
wheat  did  he  sell  ? 


136  PERCENTAGE 

Process  Explanation:  Apply  the  for- 

:48  =  48  % .   Ans.      mula  i?  =  |  •  228  bu.  is  the  per- 

475)228.00  ^ 

-1  Q/^Q  centage  and  475  bu.  is  the  base. 

QQQQ  Dividing  the  percentage  by  the 
ggQQ  base  we  get  .48  or  48  ^  ;  that  is, 
228  bu.  is  48  %  of  475  bu. 

Oral  Exercise 

148.  1.    What  per  cent  of  16  is  8  ?     Of  15  is  3  ? 
Of  16  is  4? 

2.  What  per  cent  of  24  is  18  ?     Of  30  is  25  ? 
Of  40  is  16  ? 

3.  4  is  what  %  of  5  ?  6  of  8  ?  10  of  15  ?  5  of  3  ? 

4.  $  120  is  what  %  of  $  160  ?     60  rods  is  what 
%  of  a  mile  ? 

5.  i  is  what  %  of  1?  of  I?  of  I  ?  of  2? 

6.  What  %  more  than  200  is  250  ?  240  is  300  ? 

7.  What  %  less  than  75  is  50  ?  60  is  40  ? 

Written  Exercise 

149.  1.   What  per  cent  of  6714  is  78?     Of  98 
is  64  ? 

2.  What  per  cent  of  $  12.50  is  $3  ? 

3.  What  per  cent  of  $  7487  is  $  986  ? 

4.  What  per  cent  of  72  feet  is  6.1  feet  ? 

5.  What  per  cent  of  f  is  J  ? 

6.  What  per  cent  of  484  is  86  ? 

7.  What  per  cent  of  45  is  f  ? 


CASE  II  137 

8.  What  per  cent  of  f  is  .45  ? 

9.  What  per  cent  of  24  is  9.76  ? 

10.  What  per  cent  of  27.3  is  8.57  ? 

11.  What  per  cent  of  6872  is  178.56  ? 

Written  Problems 

150.  1.  In  a  field  of  undrained  land  a  farmer  is 
able  to  raise  a  crop  of  oats  averaging  27  bushels 
per  acre.  By  tiling  the  land  the  yield  is  increased 
17^  bushels.     What  is  the  per  cent  of  gain  ? 

2.  On  ten  acres  of  ground  a  farmer  raises  184 
tons  and  600  pounds  of  sugar  beets  for  which  he 
receives  $  5  a  ton.  If  he  spends  $  200  for  labor  and 
the  land  is  worth  $150  an  acre,  what  per  cent  of 
the  value  of  the  land  is  his  net  profit  on  the  crop  ? 

3.  The  average  yield  of  wheat  in  Kansas  is  13.1 
bushels  per  acre,  in  Great  Britain  31  bushels. 
What  per  cent  greater  is  the  yield  of  wheat  in 
Great  Britain  than  in  Kansas? 

4.  A  merchant  failed  owing  $18,500,  with 
assets  of  $  7200.  What  per  cent  of  his  debts 
could  he  pay  ?     How  much  on  the  dollar  ? 

5.  Of  1000  pounds  of  green  corn  about  200 
pounds  are  dry  matter.  If  the  dry  matter  is 
burned,  the  ashes  will  weigh  about  12  pounds. 
What  per  cent  of  green  corn  is  ash  ?  What  per 
cent  is  organic  matter;  i.e.  passes  off  in  the  form 
of  smoke  ? 


138 


PERCENTAGE 


6.  The  entire  number  of  cattle  on  the  farms  and 
ranges  of  the  United  States  was  53  millions  in 
1890,  68  millions  in  1900,  and  69  millions  in  1910. 
Find  the  per  cent  of  increase  for  each  decade. 

7.  The  acreage  and  yield  of  sugar  beets  in  Kansas 
for  1911  was  4963  acres  and  27,256  tons,  and  in 
1912,  8903  acres  and  88,842  tons,  respectively. 
What  was  the  per  cent  of  increase  in  yield  per  acre  ? 

8.  The  composition  of  a  certain  bronze  alloy  is 
53  parts  by  weight  of  copper,  22J  of  nickel,  22 
of  zinc,  5  of  tin,  f  of  bismuth,  and  |  of  aluminum. 
Express  these  as  per  cents,  and  find  the  weight  of 
each  material  required  to  make  1748  pounds  of  alloy. 

9.  In  a  winter  steer  feeding  experiment,  the 
following  daily  ration  for  each  animal  was  used : 
15.40  pounds  of  shelled  corn,  2.75  pounds  of  cot- 
tonseed meal,  5.81  pounds  of  clover  hay,  and 
16.03  pounds  of  corn  silage.  Each  kind  of  feed 
was  what  per  cent  of  the  daily  ration  ? 

10.  Determine  the  percentage  standing  of  the 
national  league  baseball  clubs  for  a  recent  year  by 
filling  the  proper  column  of  the  following  table : 


Team 

Won 

Lost 

Pee 
Cent 

Team 

Won 

Lost 

Per 

Cent 

Chicago    .     . 
New  York     . 
Pittsburgh    . 
Philadelphia 

99 
98 
98 
83 

55 
56 
56 
71 

— 

Cincinnati . 
Boston  .     . 
Brooklyn    . 
St.  Louis    . 

73 
63 
53 
49 

81 

91 

101 

105 

— 

CASE  III  139 

Study  Exercise,  Case  III 

151.  Percentage  and  rate  given,  to  find  the 
base.  To  find  the  base  when  the  percentage  and 
rate  are  given,  divide  the  percentage  by  the  rate, 
expressed  as  a  decimal. 

The  formula  for  Case  III  is  ^=  ^. 

r 

1.  If  a  farm  rents  for  $  450,  or  6  %  of  its  value, 
what  is  its  value  ? 

Process  Explanation :  B  =  --     %  450  is  the  percent- 

.06)  $  450.00  ^^^  6  %  is  the  rate.     Dividing  the  per- 

^  io\j\)  centage  by  the  rate  we  obtain  the  base,  or 

value ;  hence  $  450  -e-  .06  =  $  7500,  value  of  the  farm. 

Oral  Exercise 

152.  1.  50  is  25  %  of  what  number  ? 

2.  16  is  33|^%  of  what  number? 

3.  2  is  J  %  of  what  number  ? 

4.  10  is  .3  %  of  what  number  ? 

5.  $2.50  is  121%  of  how  many  dollars? 

6.  40  gal.  is  66-|%  of  how  many  gallons? 

7.  8  ft.  Sin.  is  831%  of  what? 

8.  3  bu.  4  pk.  is  40  %  of  what  ? 

Written  Exercise 

153.  1.    12  is  20  %  of  what  number  ? 

2.  16  is  25%  of  what  number? 

3.  56  is  33  J  %  of  what  number  ? 


140  PERCENTAGE 

4.  J  is  40  %  of  what  number  ? 

5.  74  is  75  %  of  what  number  ? 

6.  93  is  49  %  of  what  number  ? 

7.  47  is  |-  %  of  what  number  ? 

8.  96  is  .5  %  of  what  number  ? 

9.  187  is  125%  of  what  number? 
10.  457  is  166|%  of  what  number? 

Written  Problems 
154.   1.    If  a  farm  rents  for  $  850,  which  is  4  % 
of  its  value,  what  is  its  value  ? 

26-1  sold  148  bushels  of  wheat,  which  was  37  % 
of  what  I  raised.     How  much  did  I  raise  ? 

3.  During  a  certain  year  of  the  tick -fever  scourge 
161,000  cattle  of  Mississippi,  or  18.5%,  died  of 
the  disease.  Find  the  number  of  cattle  in  the 
state  for  that  year, 

4.  If  the  ore  in  a  mine  yields  -f^  of  1  %  of  pure 
gold,  how  many  tons  of  ore  must  be  taken  out  to 
obtain  8  pounds  of  gold  ? 

5.  A  grocer  bought  potatoes  at  48 J^  per  bushel 
and  marked  them  so  as  to  gain  25%,  but  sold 
them  at  a  reduction  of  12^  %  from  the  marked 
price.  If  he  gained  $56.25,  how  many  bushels 
had  he  ? 

6.  A  contractor  estimates  the  actual  cost  to  him 
of  paving  a  certain  street  at  $825  per  block. 
What   should   be   the   complete    estimate   on   the 


GROUP  PROBLEMS  141 

basis  of  6%  of  the  above  amount  for  superintend- 
ing and  10  %  on  the  cost,  including  superintending, 
for  profit  ? 

7.  In  an  experiment  to  increase  the  amount  of 
butter  fat  in  milk  by  liberal  feeding,  it  was  found 
that  the  average  weekly  production  of  4.18  pounds 
of  butter  fat  per  single  cow  of  a  dairy  herd  was  in- 
creased 55%,  and  that  the  food  cost  of  18 (^  per 
day  was  increased  16|  %.  If  butter  fat  yields  f  of 
its  weight  in  butter,  find  the  increased  weekly 
profit  from  the  liberal  feeding  with  butter  at  28^ 
per  pound. 

GROUP   PROBLEMS   IN   PERCENTAGE 

Group  I.     Seeds 

155.  1.  Of  51  samples  of  clover  seed  examined 
by  the  U.  S.  Department  of  Agriculture  3  were 
heavily  adulterated  with  black  medic,  10  were  free 
from  dodder,  and  of  these  2  were  of  low  vitality. 
What  per  cent  were  entirely  fit  for  seed  ?  What 
per  cent  were  of  low  vitality  ? 

2.  In  the  vitality  test  86.6  %  was  the  average 
for  the  51  samples.  What  was  the  average  num- 
ber of  pounds  of  good  seed  to  the  bushel  ? 

3.  If  clover  seed  is  $  12  per  bushel,  what  is  the 
actual  cost  per  bushel  of  good  seed  if  86.6  %  of  the 
seed  is  good  ? 


142  PERCENTAGE 

4.  If  the  lowest  test  was  64.2%,  what  would  be 
the  actual  cost  per  bushel  of  good  seed  at  $  12  per 
bushel  ? 

5.  A  vitality  test  on  one  sample  of  seed  showed 
that  72  %  of  it  was  good.  Another  sample  tested 
showed  that  89  %  of  it  was  good.  If  the  first 
sample  was  $  10  per  bushel  and  the  second  $  14  per 
bushel,  which  would  be  the  more  expensive  to  buy 
for  good  seed  ? 

6.  If  only  90  %  of  the  wheat  required  to  sow  40 
acres  germinates,  how  many  acres  are  seeded  to 
grain  that  will  not  germinate  ? 

7.  If  8  out  of  every  10  grains  of  corn  grow, 
what  per  cent  of  the  seed  is  good  ? 

8.  The  average  loss  of  weight  of  corn  in  cribs 
at  the  Kansas  station  from  November  1  to  Janu- 
ary 31  was  5.17%.  What  would  be  the  loss  from 
shrinkage  on  1560  bushels  of  corn  if  kept  until 
January  31  ?  Which  would  be  the  more  profitable, 
to  sell  the  corn  in  November  at  55^  or  keep  it 
until  January  and  sell  it  at  65)^  per  bushel  ? 

Group  II.     Dairy  Problems 

156.  1.  If  cream  testing  25%  sells  at  60/^  per 
gallon,  what  should  be  the  price  per  pound  of 
butter  if  it  takes  |^  of  a  pound  of  butter  fat  to 
make  one  pound  of  butter  ? 

2.  If  the  butter  is  worth  30)^  per  pound,  what 
should  cream  testing  26  %  be  worth  per  gallon  ? 


GROUP  PROBLEMS  143 

3.  If  milk  tests  5.3  %  and  8  %  is  lost  in  skim- 
ming by  the  shallow-pan  method,  what  is  lost  per 
year  if  a  cow  averages  25  pounds  of  milk  per  day  ? 

4.  What  is  the  loss  if  the  deep-pan  method  is 
used  and  only  3.2  %  is  lost  ? 

5.  What  is  the  loss  if  a  hand  separator  is  used 
and  only  .3  %  is  lost  ? 

6.  A  cow  averages  20  pounds  of  milk  daily  for  a 
year.  What  will  be  the  value  of  the  butter  fat 
produced,  if  the  milk  tests  4.1  %,  at  28  j^  per  pound  ? 

7.  In  an  experiment  at  the  Wisconsin  station 
with  the  dairy  herd,  it  was  found  that  each  cow 
averaged  for  the  year  8536  pounds  of  milk  which 
yielded  4^%  of  butter  fat,  which  in  turn  was  con- 
verted into  butter,  f  of  which  was  butter  fat. 
With  the  cost  of  feed  $65.72,  and  butter  worth 
27-|i2^  per  pound,  what  was  the  profit  for  each  cow  ? 

8.  In  a  feeding  test  at  the  Illinois  station  the 
average  milk  production  per  cow  for  a  period  of 
six  weeks  was : 

Lot  I  Lot  II 

Timothy  Alfalfa  Timothy         Alfalfa 

1134  1b.  1247  1b.  829  1b.         1065  1b. 

What  was  the  per  cent  of  increase  in  milk  produc- 
tion gained  in  each  case  by  feeding  alfalfa  hay  ? 

9.  During  a  three  months'  period  one  cow  gives 
1825  pounds  of  milk  yielding  3.8%  of  butter  fat, 
and  another  gives  1460  pounds  of   milk  yielding 


144 


PERCENTAGE 


3.4  %  of  butter  fat.  The  food  cost  of  the  first  cow 
was  $5.40  per  month  and  of  the  other  8%  less. 
If  the  butter  fat  is  converted  into  J  of  its  weight 
in  butter  with  butter  at  26 1^  per  pound,  which  cow 
pays  the  more  for  the  period  and  how  much.  ? 


Group  in.    Poultry  Problems 


157.  1.  From  879  eggs  set,  533  were  hatched 
in  incubators.  What  per  cent  of  the  number 
were  hatched?     (Oregon  Experiment  Station.) 

2.  From  279  eggs,  hens  hatched  219  chicks. 
What  per  cent  of  the  eggs  were  hatched? 

3.  In  Problems  1  and  2,  78.5%  and  96.5%  of 
the  fertile  eggs  hatched.  How  many  of  the  eggs 
in  each  case  were  fertile  ? 

4.  The  mortality  of  the  hen-hatched  chicks 
raised  in  brooders  was  10.8  %  in  4  weeks,  and  of 
the  incubator-hatched  chicks  was  33.5%.  How 
many  of  the  chicks  of  Problem  2  were  living  at 


GROUP  PROBLEMS  145 

the  end  of  four  weeks  ?     Plow  many  of  those  of 
Problem  1  ? 

5.  The  mortality  of  hen-hatched  chicks  brooded 
under  hens  was  2.2  %  and  of  the  incubator-hatched 
chicks  under  the  same  conditions  of  brooding  was 
49.2%.  What  was  the  number  living  at  the  end 
of  four  weeks  in  each  case  given  above  ? 

6.  In  other  tests  the  mortality  was  46.5%  for 
incubator  chicks  brooded  by  hens  and  58.4%  for 
those  raised  by  brooders.  What  would  be  the 
number  of  survivors  in  each  case  given  above? 

7.  How  much  of  each  of  the  following  feeds 
will  a  hen  eat  in  a  year  if  fed  .175  pound  of 
grain,  .07  pound  of  ground  bone,  and  .022  pound 
of  alfalfa  meal  daily  ? 

8.  What  will  it  cost  to  keep  a  hen  a  year  if 
the  grain  is  $  1.25  per  hundred,  the  ground  bone 
1^^  per  pound,  and  the  alfalfa  meal  $  10  per  ton? 

9.  If  eggs  are  worth  22 i^  per  dozen,  how  many 
eggs  must  a  hen  lay  to  pay  for  her  feed  for  one 
year? 

10.  The  average  of  a  poultryman's  flock  of  hens 
in  1899  was  76  eggs,  and  in  1906  by  selecting  and 
breeding  it  had  increased  to  134.  What  was  the 
per  cent  of  increase  ? 

11.  The  hens  of  Kansas  average  75  eggs  per 
year.  This  is  34.25%  of  the  number  the  best 
hens  lay.     How  many  do  the  best  hens  lay? 


146  PERCENTAGE 

Group  IV.    Fertilizer  Problems 


158.  1.  A  ton  of  average  barnyard  manure  con- 
tains 10  pounds  of  nitrogen,  6  pounds  of  phos- 
phoric acid,  and  8  pounds  of  potash.  What  is  the 
per  cent  of  each  in  barnyard  manure?  What 
would  be  the  value  of  five  loads  of  manure  weigh- 
ing a  ton  each  at  the  rate  of  15l^  per  pound  for 
the  nitrogen,  5^  for  the  phosphoric  acid,  and  5^ 
for  the  potash  ? 

2.  The  amount  of  phosphoric  acid  and  potash 
found  in  the  five  loads  of  Problem  1  is  about  40  % 
of  the  amount  of  each  of  these  taken  from  the  soil 
by  a  crop  of  corn  yielding  62  J  bushels  and  5  tons 
of  stalks.  How  many  pounds  are  taken  from  the 
soil  by  the  corn  crop  ? 


GROUP  PROBLEMS  147 

3.  In  a  four  years'  series  of  experiments  with 
potatoes  at  the  New  York  station  the  yield  per 
acre  for  the  unfertihzed  plots  was  160.1  bushels, 
and  of  the  plots  treated  with  1000  pounds  of  fer- 
tilizer per  acre,  184.5  bushels.  Find  the  per  cent 
of  increase  due  to  the  fertilizer. 

4.  The  following  results  show  the  effects  of 
different  fertilizers  upon  the  yield  of  rauskmelons 
at  the  Illinois  station.  No  manure,  188  baskets  per 
acre;  manure  broadcast,  400;  manure  broadcast  and 
in  the  hills,  596 ;  steamed  bone  in  the  hills,  305 ; 
manure  and  rock  phosphate  in  the  hills,  575.  Each 
basket  contains  16  pounds  of  fruit.  Find  the  per 
cent  of  increased  yield  due  to  each  fertilizer. 

5.  At  the  New  York  station  the  average  annual 
yield  of  timothy  hay  per  acre  under  various  modes 
of  treatment  has  been :  No  treatment,  3600 
pounds  per  acre ;  320  pounds  of  acid  phosphate, 
4233 ;  80  pounds  of  potash,  4490 ;  160  pounds  of 
nitrate  of  soda,  4530 ;  and  10  tons  of  manure, 
5093.  Find  the  per  cent  of  increase  in  yield  per 
acre  due  to  each  fertilizer.  Also  find  the  net 
profit  from  each  treatment  at  the  following  scale 
of  prices :  acid  phosphate,  $  14  per  ton ;  muriate 
of  potash,  $  40  per  ton ;  nitrate  of  soda,  $  50  per 
ton;  manure,  50^  per  ton;  hay,  $14.50  per  ton. 

6.  A  ton  of  fertilizer  for  corn  land  contains 
45%  cottonseed   meal    at    $30.50   per   ton,   with 


148 


PERCENTAGE 


93  %  of  the  remaining  portion  consisting  of  acid 
phospiiate  at  $  15.25  per  ton  and  the  rest  muriate 
of  potash  at  $45.60  per  ton,  respectively.  Find 
the  cost  of  the  fertilizer. 

7.  In  a  wheat-fertilizing  experiment  at  the 
Indiana  station  the  following  results  per  acre  were 
obtained : 


Nitrogen,  phosphorus,  potash 
Phosphorus,  potash  .... 
Nitrogen,  potash 


Value  of 

Increased 

Yield  at  86^ 

PER  Bushel 

Fertilizer 
Cost 

$6.75 
4.04 
2.65 

$5.19 
2.75 
3.38 

Profit  or 
Loss  per 
Acre  per 
Dollar 
Invested 


Fill  the  blanks  and,  from  the  percentage  results 
of  the  last  column,  note  the  relative  value  of  the 
fertilizers. 

8.  What  per  cent  of  nitrogen,  phosphoric  acid, 
and  potash  will  there  be  in  a  ton  of  fertilizer  com- 
posed as  follows :  700  pounds  of  acid  phosphate, 
800  pounds  of  bone  meal,  500  pounds  of  muriate 
of  potash  with  composition  of  the  fertilizing 
materials  taken  as  14  %  phosphoric  acid,  3.8  % 
nitrogen  plus  25.6%  phosphoric  acid,  and  50% 
potash,  respectively? 

9.  How  many  pounds  of  nitrogen,  phosphoric 
acid,  and  potash  will  there  be  in  a  ton  of  fertilizer 
composed  as  follows :  1200  pounds  of  acid  phos- 
phate   containing     14%     phosphoric    acid;     300 


GROUP  PROBLEMS  149 

pounds  of  potash,  50  %  pure ;  250  pounds  of  bone 
meal,  3  %  nitrogen  and  22  %  phosphoric  acid ;  and 
250  pounds  of  filler  ? 

10.  If  cheese  is  3.9%  nitrogen,  .6J%  phos- 
phorus, and  Y2'^  potash,  how  many  pounds  of 
each  are  sold  in  a  ton  of  cheese  ? 

11.  If  butter  is  J-%  nitrogen,  ^%  phosphoric 
acid,  and  -^^o  potash,  how  many  pounds  of  each 
are  sold  with  a  ton  of  butter  ? 

12.  If  beef  is  2.5  %  nitrogen,  1.9  %  phosphoric 
acid,  and  f%  potash,  what  is  the  number  of 
pounds  of  each  in  a  ton  of  beef? 

13.  A  bushel  of  wheat  contains  2.1%  of  nitro- 
gen, 1.1%  phosphoric  acid,  and  .6%  potash. 
How  many  pounds  of  each  are  removed  from  the 
farm  with  every  ton  of  wheat  sold  ? 

14.  A  bushel  of  corn  contains  1.4  %  of  nitrogen, 
.5  %  of  phosphoric  acid,  and  .5  %  of  potash.  How 
many  tons  of  each  are  removed  from  the  farm 
with  every  ton  of  corn  sold? 

15.  In  a  ton  of  wheat  straw  there  are  about 
J  %  of  nitrogen,  |-  %  of  phosphoric  acid,  and  f  % 
potash.  What  would  be  the  loss  in  pounds  of  fer- 
tilizing substances  if  the  straw  was  sold  ? 

16.  If  an  acre  of  land  when  manured  yields  11|^ 
bushels  of  wheat  and  when  treated  with  manure  and 
rock  phosphate  yields  15  bushels,  what  is  the  per 
cent  of  increase  due  to  the  use  of  the  phosphate  ? 


150 


PERCENTAGE 


17.  The  fertilizing  value  of  average  fresh 
manure  is  about  $  2.25  per  ton,  and  after  leaching 
two  or  three  months  in  heavy  rains  it  is  worth 
about  $  1.50  per  ton.    What  is  the  per  cent  of  Ipss  ? 

18.  In  a  series  of  experiments  on  corn,  wheat, 
oats,  and  potatoes  it  was  found  that  one  ton  of 
fresh  manure  produced  an  average  increase  in 
crop  value  of  $  2.96  and  when  exposed  three 
months  yielded  an  increase  of  $2.15.  Find  the 
per  cent  of  loss  in  fertilizing  value. 

Group  V.    Spraying  Problems 

159.  1.  Two  farmers  plant  an  acre  of  potatoes 
each.  One  sprays  for  the  blight  and  gets  a  yield 
of  200  bushels ;  the  other  does  not  spray  and  gets 
85  bushels.  What  was  the  per  cent  of  increase 
due  to  spraying  ? 

2.    In  an  experiment  for  control  of  apple  blotch, 
the  following  table  exhibits  data  and  partial  results: 


Block 

I 

Trees  Sprayed 

Total  Yield 

Affected 
BY  Blotch 

Per  Cbnt 

No.  1 

1331 

38 

— 

No.  2 

3464 

62 

— 

No.  3 

2551 

80 

— 

No.  4 

3227 

83 

— 

Total 

— 

— 

— 

Averages 

— 

— 

— 

GROUP  PROBLEMS 


151 


Block  II 

Tkeks  Unspkated 

Total  Yield 

Affected  by 
Blotch 

Ter  Cent 

No.  1 

4287 

288 



No.  2 

5858 

969 

— 

No.  3 

1742 

201 



No.  4 

2182 

171 

— 

No.  5 

1467 

182 

— 

Total 

— 

— 

— 

Averages 

— 

— 

— 

Fill  the  blanks  and  note  the  effect  of  spraying 
by  comparison  of  the  average  per  cents. 


SPRAYED 


UNSPRAYED 


On«$      Twos     Culls         Ones     Twos      Culls 


3.    In   an   apple    tree    pruning  experiment,  the 
following   results   in   fruit   yield  in   bushels  were 


152  PERCENTAGE 

obtained :  from  an  unpruned  set  of  five  trees, 
2.37  bushels  of  fancy  grade,  15.77  bushels  of  ones, 
12  bushels  of  twos,  2.25  bushels  of  culls;  from 
a  pruned  set  of  five  trees  in  the  same  orchard  5.94 
bushels  of  fancy  grade,  15.25  bushels  of  ones,  4.05 
bushels  of  twos,  and  1.08  bushels  of  culls.  Deter- 
mine for  each  grade  in  each  set  of  trees  its  per  cent 
of  the  total  yield,  and  thus  note  the  effect  of  pruning 
by  a  comparison  of  the  same  grade  in  the  two  sets. 

4.  Under  ordinary  circumstances  the  average 
yield  of  merchantable  apples  can  be  increased 
about  4  bushels  per  tree.  This  gives  a  net  profit 
of  $  1.62  per  tree.  What  is  the  per  cent  of  profit 
if  apples  are  worth  80^  per  bushel  ? 

5.  The  average  per  cent  of  increase  in  Problem 
4  was  37%  of  the  sprayed  over  the  unsprayed. 
What  was  the  original  yield  ? 

Group  VI.    Soils 

160.  1.  By  separating  a  clay  soil  into  its  con- 
stituent parts,  it  is  found  that  about  .2  %  is  fine 
gravel,  .3  %  is  coarse  sand,  .4  %  is  medium  sand, 
1.5%  is  fine  sand,  3.1%  is  very  fine  sand,  58.2% 
is  silt,  and  36.3  %  is  clay.  What  amount  of  each 
is  found  in  a  cubic  foot  of  soil  weighing  65  lb.  ? 

2.  The  composition  of  sandy  loam  is  as  fol- 
lows :  1.3  %  fine  gravel,  3.3  %  coarse  sand,  4.3  % 
medium  sand,  17.5%  fine  sand,  21.5%  very  fine 
sand,  17.5%   silt,  and  14.3%  clay.     What  amount 


GROUP  PROBLEMS 


153 


of   each  is  found  in  a    cubic  foot  of   sandy  loam 
weighing  87  pounds  ? 

3.  The  composition  of  a  silt  loam  is  as  follows : 
.8%  fine  gravel,  5.1%  coarse  sand,  4%  medium 
sand,  5%  fine  sand,  6.3%  very  fine  sand,  60.7% 
silt,  and  18.1  %  clay.  Find  the  amount  of  each  con- 
tained in  a  cubic  foot  of  soil  weighing  75  pounds. 

4.  An  analysis  of  Minnesota  prairie  loam  to 
determine  the  amount  of  plant  food  constituents 
found  in  the  soil  showed  the  following  results : 
.16%  phosphoric  acid,  .83%  lime,  .35%  magnesia, 
.43  %  soda,  and  .4  %  potash.  Find  the  number  of 
pounds  of  each  of  these  found  in  a  one-acre  foot 
of  soil,  if  one  cubic  foot  of  soil  weighs  80  lb. 

5.  An  analysis  of  Ohio  silt  loam  to  determine 
the  amounts  of  plant  food  gave  the  following 
results:  .09%  phosphoric  acid,  .18%  lime,  .5% 
magnesia,  .29  %  soda,  and  .21  %  potash.  Find  in 
thousand  pounds  the  amounts  of  each  of  these  in 
one-acre  foot  of  soil  whose  estimated  weight  is  3.5 
million  pounds. 

6.  Determine  the  maximum  water  capacity  of 
the  various  soils  listed  in  the  following  table : 


Name  of  Soil 


Coarse  sand .  . 
Light  silt  loam 
Clay  .  .  .  . 
Humus     .     .     . 


Total   Weight 
PER  Cubic  Foot 

81 

83 


15 


Weight  of  Water 
IN  1  Cv.  Ft. 

32.0 
31.5 
37.0 
50.0 


%  OF  Water  at 
Saturation 


GAIN  AND  LOSS 

161.  The  one  fundamental  thing  to  be  remem- 
bered in  figuring  gain  and  loss  in  a  business  trans- 
action, is  the  fact  that  the  gain  or  loss  is  always 
reckoned  on  the  cost  or  the  sum  invested.  There 
is  a  very  close  relation  between  the  terms  of  profit 
and  loss  and  those  of  percentage.  The  cost  is  the 
base,  the  per  cent  of  gain  or  loss  is  the  rate,  the  gain 
or  loss  is  the  percentage,  and  the  selling  price  is 
the  amount  or  difference. 

Formulas  :  Cost  x  rate  =  gain  or  loss,  or  P  =  hr. 
Gain  or  loss  h-  cost  =  rate,  or  i?  =  -^. 

0 

Gain  or  loss  -^  rate  =  cost,  or  B  =^. 

r 

Cost  +  gain  or  loss  =  selling  price. 

If  one  formula  is  given,  can  you  develop  the 
others?     Show  how  to  do  it. 

Oral  Exercise 

162.  1.  Goods  costing  $  212.25  were  sold  at  a 
profit  of  33J%.     What  was  the  profit? 

2.  A  horse  costing  $150  was  sold  for  $180. 
What  was  the  per  cent  of  gain  ? 

154 


WRITTEN  PROBLEMS  155 

3.  In  order  to  gain  10%,  at  what  price  must  I 
sell  a  horse  which  cost  $  120  ? 

4.  A  farm  sold  for  $7150  at  a  profit  of  10%. 
What  was  the  cost? 

5.  On  account  of  a  delay  in  shipping,  plums  that 
cost  $1  a  crate  were  sold  at  SO^.  What  was  the 
per  cent  of  loss  ? 

6.  Butter  that  cost  30^  a  pound  was  sold  for 
33^.     What  was  the  per  cent  of  profit? 

Written  Problems 

163.  1.  A  man  bought  a  horse  for  $180  and 
sold  it  at  a  profit  of  18  %.  What  was  the  selling 
price  and  what  was  the  profit  ? 

2.  A  farmer  bought  100  sheep  at  $5  per 
head.  From  these  he  raises  96  lambs  worth  $5 
each.  If  it  costs  $2.90  each  to  feed  the  sheep  a 
year,  what  is  the  per  cent  of  profit  on  the  original 
investment  ? 

3.  A  hot-water  heating  plant  for  an  eight-room 
house  will  cost  about  $480.  A  hot-air  heating 
system  can  be  installed  for  $175.  If  the  better 
equipment  saves  3  tons  of  coal  worth  $  7.25  per  ton 
each  year,  what  per  cent  is  realized  yearly  on  the 
extra  amount  invested  ? 

4.  If  a  house  is  sold  for  ^  its  cost,  what  is  the 
loss  per  cent  ? 


156  GAIN  AND  LOSS 

5.  A  dealer  buys  apples  at  $2.50  per  barrel  (3  bu.) 
and  retails  them  at  30  ^  per  peck.  Find  his  gain  or 
loss  on  40  barrels  allowing  12%  for  loss  by  decay. 

6.  A  merchant  makes  a  retail  profit  of  25%. 
If  he  sells  at  wholesale  for  10  %  discount  from  the 
retail  prices,  what  per  cent  profit  does  he  make? 

7.  A  renter  raises  corn  on  38  acres  of  $50  per 
acre  land.  With  a  yield  of  60  bushels  per  acre  at 
45)^  per  bushel,  an  annual  rental  of  4J%  of  the 
farm  value,  and  a  cost  of  crop  production  amount- 
ing to  $5.50  per  acre,  how  much  profit  does  he 
make?     What  is  the  per  cent  of  profit? 

8.  With  the  conditions  of  Problem  7,  the  crop 
weighing  80  tons,  and  the  cost  of  marketing  $3 
per  ton,  find  the  profit  and  the  per  cent  of  profit. 

9.  What  per  cent  does  a  grocer  gain  by  using 
a  false  weight  of  15^  ounces  for  a  pound?  What 
per  cent  does  the  customer  lose  ? 

10.  A  quantity  of  oats  was  sold  in  succession  by 
three  dealers,  each  of  whom  made  a  profit  of  4%. 
The  last  dealer  received  $  2756.  How  much  did  it 
cost  the  first  ? 

11.  A  house  is  valued  at  $4500  and  rents  at 
$30  per  month.  The  yearly  repairs  amount  to 
$60,  and  the  taxes  and  insurance  to  $42.50.  What 
per  cent  on  the  investment  does  the  property  pay  ? 

12.  A  farm  worth  $5000  with  buildings  valued 
at  $1200,  stock  and  machinery  at  $1500,  yields 


WRITTEN  PROBLEMS  157 

an  annual  return  of  $1800.  Counting  the  rise 
in  land  value  at  3%,  depreciation  and  repairs  of 
buildings  at  5  %,  depreciation  of  stock  and  machin- 
ery at  6%,  taxes  and  insurance  at  $70,  labor  at 
$300,  other  expenses  at  $250,  what  is  the  amount 
of  gain  ?  the  per  cent  of  gain  ? 

13.  A  man  bought  a  tract  of  land  for  $3000 
with  a  frontage  of  20  rods  and  depth  of  150  feet 
and  cut  it  up  into  residence  lots  having  a  65-foot 
front  for  the  corner  lots  and  a  50-foot  front  for 
each  of  the  others.  One  year  later  he  sold  the 
corner  lots  for  $1200  each  and  the  others  at  $1000 
each,  having  in  the  meantime  paid  an  average  of 
$20  a  lot  for  taxes  and  $4  a  running  front  foot 
for  sidewalks  and  paving.  What  was  the  gain  ? 
The  per  cent  of  gain  ? 

14.  A  man  sold  two  houses  for  $4000  each.  On 
one  he  gained  25  %,  and  on  the  other  he  lost  25  %. 
What  was  the  gain  or  loss  on  the  whole  transac- 
tion ?     What  was  the  per  cent  of  gain  or  loss  ? 

15.  The  average  annual  depreciation  of  the  first 
cost  of  a  mower  costing  $45  is  7.8%  ;  of  a  grain 
binder  costing  $145  is  7.91  %  ;  of  a  corn  binder  cost- 
ing $125  is  10.03  %.  What  is  the  average  annual 
depreciation  of  each  ? 

16.  A  manure  spreader  cost  $125.  It  has  been 
used  7  years  and  is  now  valued  at  $33.  What  is 
the  annual  per  cent  of  depreciation  based  upon  the 
first  cost  ? 


COMMISSION 
Study  Exercise 

164.  A  person  who  buys  or  sells  goods  or  who 
transacts  business  for  another  person  is  called  a 
commission  merchant  or  agent. 

The  agent's  pay  is  usually  reckoned  at  a  certain 
per  cent  of  the  amount  of  the  transaction  and  is 
called  the  commission. 

The  total  amount  received  by  the  agent  for  the 
sales  is  the  gross  proceeds. 

The  prime  cost  is  the  actual  cost  of  the  articles. 

The  sum  left  after  the  commission  has  been  paid 
is  called  the  net  proceeds. 

The  principles  of  percentage  applied  here  may  be 
expressed  in  formulas  as  follows : 

Formulas :  Commission  =  gross  proceeds  or  prime 
cost  X  rate  of  commission, 

Rate  of  commission  =  commission  ^  gross  proceeds 
or  prime  cost,  ^ 

^      b 

Gross  proceeds  or  prime  cost  =  commission  ^  rate 
of  commission,  ^ 

r 

168 


WRITTEN  PROBLEMS  159 

Oral  Exercise 

165.  1.  The  gross  proceeds  of  a  sale  are  $  360, 
rate  3  % .     What  is  the  commission  ? 

2.  The  prime  cost  is  $  1250,  rate  21  %.  What  is 
the  commission  ? 

3.  The  commission  is  $  9.50,  gross  proceeds  $  380. 
What  is  the  rate  ? 

4.  The  commission  is  $  18,  the  prime  cost  1 1200. 
What  is  the  rate  ? 

5.  The  commission  is  $20  and  the  rate  2J%. 
What  is  the  prime  cost  ? 

6.  The  commission  is  $12.80  and  the  rate  |%. 
What  are  the  gross  proceeds  ? 

Written  Problems 

166.  1.  If  I  send  a  coop  of  2  dozen  young 
chickens,  averaging  3  pounds  each,  to  St.  Louis  and 
a  commission  firm  sells  them  at  29 j^  per  pound, 
charging  a  commission  of  8%,  and  paying  50^  ex- 
press, what  do  I  receive  per  pound  for  the  chickens  ? 

2.  A  fruit  grower  sends  75  barrels  of  apples  to 
a  commission  merchant,  who  sells  them  at  $2.50 
per  barrel.  His  commission  is  5  %  and  the  freight  is 
35j^  per  barrel.  What  will  the  fruit  grower  receive 
per  barrel  for  the  apples  ? 

3.  A  dairyman  sent  his  city  agent  during  a  certain 
month  975  pounds  of  butter.  If  the  agent's  commis- 
sion was  2J%,  the  delivery  charges  $  10.35,  selling 


/ 


160  COMMISSION 

price  per  pound   34^,  what  was  the  amount  the 
dairyman  received  per  pound  for  his  butter  ? 

4.  A  city  merchant  sent  his  agent  in  Missouri 
$  1200  with  which  to  buy  apples  at  65)2^  per  barrel 
and  pay  his  commission  of  S^%  and  Qf^  per  barrel 
for  drayage.     How  many  barrels  did  he  buy  ? 

5.  A  dairyman  received  $  715  as  the  net  pro- 
ceeds of  a  shipment  of  butter.  If  the  agent's 
commission  was  2  %,  storage  and  delivery  charges 
$  20,  how  many  pounds  were  sold  at  30^  per  pound  ? 
What  was  the  agent's  commission  ? 

6.  A  farmer  ships  three  cars  of  baled  alfalfa 
hay,  each  car  containing  12  tons,  to  a  commission 
merchant  in  Kansas  City,  who  sells  it  for  $  14.50 
per  ton.  After  paying  50^  per  car  switching 
charges,  50  j^  per  car  inspection  charges,  $  12  freight, 
and  receiving  50 1^  per  ton  commission  for  selling, 
what  will  be  the  net  proceeds  for  the  farmer  ? 

7.  What  per  cent  of  the  gross  receipts  are  the 
charges  connected  with  the  selling  of  the  hay  in 
Problem  6  ? 

8.  If  the  commission  for  selling  the  hay  in 
Problem  6  be  increased  50%,  what  will  be  the  net 
proceeds  ? 

9.  A  live  stock  dealer  ships  a  bunch  of  69  hogs, 
weighing  16,580  pounds,  to  Kansas  City,  and  the 
commission  man,  after  deducting  80  pounds  for 
shrinkage,  sells  the  lot   for    $  6.35   per  hundred. 


WRITTEN  PROBLEMS  161 

After  paying  $  25.50  for  freight,  including  feed  on 
the  road,  $  4.14  for  yardage,  for  2  bushels  of  corn  at 
$  1.10  per  bushel,  and  charging  $  8  for  selling,  what 
is  the  amount  of  the  check  returned  to  the  shipper  ? 

10.  A  stockman  ships  a  carload  of  26  steers, 
averaging  1520  pounds  each,  to  Kansas  City,  and 
the  commission  dealer  sells  them  at  $  8.75  per  hun- 
dred. After  paying  $  21  for  freight,  including  feed 
on  the  road,  $4.70  for  yardage,  for  400  pounds  of 
hay  at  $  15  per  ton,  for  200  pounds  of  com  at  $  1 
per  bushel,  and  charging  60 i^^  a  head  for  selling, 
find  the  net  amount  sent  to  the  shipper. 

11.  A  live  stock  man  ships  a  carload  of  63  hogs, 
weighing  325  pounds  each,  to  Chicago;  and  the  com- 
mission merchant  sells  them  for  $  8.35  per  hundred- 
weight. Find  the  amount  of  the  check  sent  to  the 
shipper  after  settlement  of  the  following  expense  ac- 
count: $  19.50  freight,  including  feed  on  the  road, 
$3.78  yardage,  3  bushels  of  com  at  90;^  per  bushel, 
20^  uispection  per  head,  20^  a  head  commission 
for  selling. 

12.  The  market  quotation  on  apples  for  a  certain 
day  was  $3.65  a  barrel.  After  receiving  275  bar- 
rels, a  falling  market  made  it  necessary  for  the  com- 
mission firm  to  sell  them  at  $  3.45.  If  the  freight 
was  15^  a  barrel,  drayage  10^  a  barrel,  and  com- 
mission 5%,  what  was  the  loss  in  net  proceeds  due 
to  the  change  in  the  market  ? 


TAXES 

167.  Money  levied  by  the  government  for  its 
support  is  called  a  tax.  Taxes  are  collected  chiefly 
from  two  classes  of  property,  —  real  estate  and  per- 
sonal property.  Real  estate  includes  land  with  its 
improvements  and  buildings.  Personal  property 
refers  to  movable  property,  such  as  furniture,  live 
stock,  merchandise,  money,  notes,  etc. 

A  poll  tax  is  a  tax  laid  upon  each  voter  re- 
gardless of  property  owned.  An  assessor  is  a 
person  who  makes  the  valuation  of  property  for 
purposes  of  taxation.  Tax  rates  on  real  or  per- 
sonal property  are  usually  expressed  as  a  rate 
per  cent  or  as  a  certain  number  of  mills  or  cents 
on  the  dollar,  and  are  based  upon  the  assessed 
valuation. 

Money  raised  by  taxes  is  expended  in  the  state 
for  the  maintenance  of  schools  and  other  institutions 
under  state  control.  In  the  counties  money  must 
be  spent  to  build  roads  and  bridges,  to  take  care  of 
the  poor,  and  to  provide  for  a  great  many  other 
things.  These  expenses  are  met  by  the  taxes  col- 
lected. Besides  the  county  expenses  there  are  those 
of  the  township  or  the  city,  to  which  must  also  be 
added  the  school  tax. 

162 


ORAL  EXERCISE  163 

How  are  the  expenses  of  the  national  govern- 
ment met  ? 

Solutions  of  problems  in  taxes  depend  upon  the 
principles  of  percentage. 

The  assessed  valuation  is  the  base. 

The  rate  of  taxation  is  the  rate. 

The  tax  is  the  percentage. 

Study  Exercise 

168.  1.  The  assessed  valuation  of  a  farm  is 
$  6000  ;  personal  property,  $  1500.  What  are  the 
taxes  at  the  rate  of  .9  %  ? 

Process  and  Explanation 
$6000  +  $1500  =  $7500,  or  total  assessed  valuation. 
.9  %  of  $7500  =  .009, X  $7500  =  $67.50,  the  taxes.   Ans. 

Oral  Exercise 

2.  A  tax  of  5  mills  on  the  dollar  is  how  much  on 
$100? 

3.  A  tax  of  li  %  is  how  much  on  $  1000  ? 

4.  At  $  1.60  a  hundred  what  is  the  tax  on  $  7500  ? 

5.  The  assessed  valuation  of  a  property  is  $  3500, 
rate  1.25%.     What  are  the  taxes? 

6.  The  taxes  on  a  farm  are  $75;  the  assessed 
valuation  $  6000.     What  is  the  rate  ? 

7.  The  taxes  on  a  property  are  $  35,  rate  $  1.75 
per  hundred.     What  is  the  assessed  valuation  ? 


164  TAXES 

Written  Problems 

169.  1.  What  is  the  tax  on  a  house  and  lot  val- 
ued at  $  2000  if  it  is  taxed  at  f  of  its  value  at 
$1.50  per  $100? 

2.  A  quarter  section  of  land,  valued  at  $  85  per 
acre,  is  taxed  at  |-  of  its  value  at  the  rate  of  70^ 
per  $  100.     What  is  the  total  amount  of  the  taxes  ? 

3.  A  city  house  and  lot  with  an  assessed  valua- 
tion of  $  3500  is  taxed  2J%.  What  is  the  amount 
of  the  tax  ? 

4.  The  property  in  a  village  is  valued  at  $650,- 
000  and  the  amount  of  revenue  to  be  raised  is 
$5200.  What  is  the  tax  on  property  assessed  at 
$  7250  ? 

5.  A  farmer  has  160  acres  of  land  assessed  at 
$  35  per  acre,  with  buildings  valued  at  $  2800. 
He  has  personal  property  amounting  to  $  2400,  of 
which  $  700  is  exempt  by  law.  Find  his  total  tax 
at  9  J  mills. 

6.  In  a  certain  township  the  value  of  the  per- 
sonal property  is  $  7500  and  that  of  the  real  estate 
is  $  1,860,000.  The  former  is  taxed  at  ;|  of  its 
value,  and  the  latter  at  ^  of  its  value.  Find  the 
amount  of  the  taxes,  the  rate  being  26.7  mills. 

7.  A  farmer  living  in  a  certain  county  owns 
120  acres  of  land  worth  $80  per  acre,  live  stock 
worth  $  1400,  and  other  personal  property  amount- 


WRITTEN  PROBLEMS  165 

ing  to  $1750.  The  personal  property  is  taxed  at 
I  of  its  value  and  the  real  estate  at  J  of  its  value. 
What  is  the  general  tax  ? 

(The  general  tax  levy  for  this  county,  in  addi- 
tion to  the  township  and  school  district  levies,  is 
apportioned  as  follows :  state,  1.20  mills ;  county, 
1.53  mills;  interest  on  bonds,  .77  mills;  road,  .50 
mills.) 

8.  His  township  levy  for  general  and  road  pur- 
poses is  .75  and  .175  mills,  respectively.  What  is 
his  entire  township  tax  ? 

9.  His  school  district  levy  is  2.30  mills.  Find 
the  school  tax  and  his  entire  tax. 

10.  A  city  in  the  above  county  has  a  local  tax  of 
7  mills  and  a  school  tax  of  6  mills.  One  of  its 
citizens  owns  property  having  an  assessed  valuation 
of  $  12,500,  has  an  income  of  $  6000,  on  which  he 
pays  an  income  tax  of  1  %  on  all  over  $  4000,  and 
pays  a  poll  tax  of  $  3.  Find  the  amount  of  his 
local  tax,  school  tax,  and  of  his  entire  tax. 

11.  The  rate  of  taxation  is  9  mills  on  the  dollar. 
What  is  the  value  per  acre  of  a  320  acre  farm  upon 
which  the  tax  is  $163.20  if  it  is  assessed  for  J  its 
value  ? 

12.  In  some  states  tax  collectors  get  a  commis- 
sion of  21  %  for  collecting.  If  the  net  amount  of 
a  tax  collection  for  a  township  was  $  7824.80,  what 
amount  was  collected  and  what  was  the  commission? 


INSURANCE 


Study  Exercise 

170.  Insurance  is  a  contract  for  protection 
against  loss.  There  are  two  principal  kinds  of 
insurance,  property  insurance  and  life  insurance. 
Property  insurance  usually  protects  against  loss  by 
fire  or  water,  and,  in  the  case  of  live  stock,  against 
loss  by  death. 

The  written  contract  between  the  insurance  com- 
pany and  the  insured  is  the  policy.  The  amount 
to  be  paid  for  the  protection  is  called  the  premium. 
The  rate  of  insurance  is  usually  stated  as  so  many 
per  cent,  or  so  much  per  $  100. 

The  amount  of  premium  in  life  insurance  depends 
upon  the  age  of  the  person  insured  and  the  kind  of 
policy.  A  partial  list  of  the  rates  for  the  three 
most  common  policies  for  a  certain  company  is 
given  in  the  following  table : 


Age 

Okdinary  Life 

20-Payment  Life 

20- Year  Endowment 

21 

$  18.50 

128.30 

$47.70 

25  , 

20.26 

30.17 

48.10 

28 

21.73 

31.76 

48.47 

30 

22.90 

32.92 

48.78 

35 

26.48 

36.27 

49.80 

40 

31.12 

40.43 

51.83 

166 


WRITTEN  PROBLEMS  167 

The  principles  of  percentage  apply  in  insurance. 
The  face  of  the  policy  is  the  base. 
The  rate  of  premium  is  the  rate. 
The  premium  is  the  perGentage. 

Written  Exercise 

171.  1,  A  house  is  insured  for  $  3500  at  the  rate 
of  35  ^  a  hundred  per  year.  What  is  the  annual 
premium  ? 

Process  and  Explanation 

$  3500  =  35  hundred  dollars. 

35  X  $  .35  =  $  12.25,  the  premium.     Ans. 

2.  If  a  house  is  insured  for  $6000  at  35;^  a 
hundred,  what  is  the  premium  ? 

3.  The  premium  for  three  years  is  twice  that 
for  one  year.  What  is  the  average  annual  premium 
for  the  house  in  Problem  2  ? 

4.  The  premium  for  five  years  is  three  times 
that  for  one  year.  What  is  the  average  annual 
premium  for  the  house  in  Problem  2  ? 

5.  What  would  be  the  premium  on  a  $3500 
policy  at  the  rate  of  J  %  per  year  ? 

■6.  What  is  the  premium  on  a  policy  of  $  3000 
taken  at  the  age  of  30  for  the  ordinary  life  ?  20- 
payment  life  ?    20-year  endowment  ? 

7.  If  a  $5000,  20-payment  life  policy  is  taken 
out  at  21  years  of  age,  what  is  the  total  amount 
paid  by  the  policy  holder  ? 


168  INSURANCE 

Written  Problems 

172.  1.  If  a  house  is  insured  for  $1500  for  3 
years  at  70  i^  per  $100,  what  is  the  premium  ? 

2.  The  insurance  rate  for  a  house  valued  at 
$4200,  having  fire  protection,  is  35^  per  $100  for 
one  year,  twice  that  amount  for  three  years,  and 
three  times  that  amount  for  5  years.  What  will 
be  the  premium  for  one  year  if  the  house  is  insured 
for  f  its  value  ?     For  three  years  ?     For  five  years  ? 

3.  A  house  cost  $9000  and  was  insured  for  |  of 
its  value  at  $1.25  per  hundred  for  5  years.  What 
was  the  premium  ? 

4.  Buildings  insured  against  fire  for  $3500  at 
the  rate  of  60^  per  $100  are  damaged  to  the  ex- 
tent of  $4850.  What  is  the  entire  loss  to  the 
owner  ? 

5.  A  farmer  pays  a  premium  of  $58.75  for  in- 
suring his  oats  for  J  of  their  value  at  1J%.  What 
is  the  value  of  the  oats  ? 

6.  A  merchant  pays  a  premium  of  85  ^  per  $100 
on  his  stock,  valued  at  $  34,500  and  insured  at  f 
of  its  value.  If  the  goods  are  entirely  destroyed 
by  fire,  what  is  his  real  loss  ? 

7.  A  grain  dealer  bought  6000  bushels  of  wheat 
and  had  it  insured  for  75  %  of  its  cost  at  3  %. 
His  premium  was  $  121.50.  At  what  price  per 
bushel  must  he  sell  it  in  order  to  gain  6  %  on  the 
total  cost  ? 


WRITTEN  PROBLEMS  169 

8.  Find  the  premium  at  the  age  of  35  for  a 
$  3500  ordinary  life  policy ;  20-payment  life. 

9.  How  much  will  a  man  have  paid  in  on  a 
20-year  endowment  policy  if  taken  out  at  the  age 
of  21,  the  face  of  the  policy  being  S2500  ? 

10.  If  a  man  takes  out  a  $  3500  policy  in  one 
company  at  $24.60  per  thousand,  and  a  $4500 
policy  in  another  company  at  $25.50  per  thousand, 
find  the  premiums. 

11.  If  a  man  pays  $67.50  annually  on  a  $3000 
policy,  what  is  the  rate  ? 

12.  A  man  takes  out  an  $8000  ordinary  life 
policy,  paying  an  annual  premium  of  $24.50  per 
thousand.  He  dies  just  before  the  15th  payment  is 
due.  How  much  will  his  estate  receive  above 
what  he  paid  the  company  ? 

13.  A  cargo  of  coffee  costing  $  28,000  is  insured 
at  the  rate  of  1J%  for  the  amount  which  will 
cover  the  cost  of  the  coffee  and  the  premium. 
Find  the  face  of  the  policy. 

14.  A  grain  dealer  in  Chicago  ordered  his  agent 
at  Duluth  to  buy  5000  bushels  of  wheat  at  65  (^, 
4500  bushels  at  50^,  6500  bushels  at  55^,  paying 
2^  %  commission  for  buying.  The  grain  was 
shipped  down  the  lakes,  and  a  policy  at  1^  %  was 
taken  out  to  cover  the  cost  of  the  grain  and  com- 
mission. Find  the  amount  of  the  policy  and  the 
premium. 


INTEREST 

173.  Interest,  as  the  term  is  commonly  em- 
ployed, is  the  sum  paid  for  the  use  of  money. 
It  is  usually  reckoned  by  taking  a  certain  per 
cent  of  the  amount  loaned  for  the  period  of  one 
year. 

The  principal  is  the  sum  loaned.  The  rate  of 
interest  is  the  per  cent  of  the  principal  paid  for  one 
year.  The  amount  is  the  sum  of  the  principal  and 
interest.  The  legal  rate  is  the  rate  established  by 
law ;  and  it  can  be  collected  when  no  rate  is  speci- 
fied in  the  contract.  The  legal  rate  varies  in  dif- 
ferent states. 

Usury  is  interest  charged  in  excess  of  that 
allowed  by  law.  Various  penalties  for  taking 
usury  are  prescribed  in  most  of  the  states.  Simple 
interest  is  interest  on  the  principal  only. 

In  interest  a  new  factor,  time,  is  introduced  into 
the  problem. 

The  relation  that  exists  between  the  various 
factors  in  interest  may  be  shown  in  formulas  as 
follows : 

Interest  =  principal  x  rate  x  time  (in  years). 
/=  prt. 

170 


SIMPLE  INTEREST  METHOD  171 

Principal  =  interest -^  (rate  x  time). 

rt 
Time  =  interest  -^  (principal  x  rate). 

rri fc 

pr 
Rate  =  interest  h-  (principal  x  time). 

pt 
Amount  =  principal  ■+•  interest. 
A  =p  +prt. 

SIMPLE   INTEREST   METHOD 

174.  Interest  is  computed  in  various  ways. 
Usually,  for  periods  less  than  one  year,  interest  is 
reckoned  on  the  basis  of  30  days  to  the  month  and 
12  months  to  the  year,  or  360  days  to  the  year. 

1.  Find  the  interest  on  $625.50  at  5  %  for  4 
years,  7  months,  and  20  days. 

Process 

Interest  fori  year  is  $625.50  x  .05  .     ...  $   31.275 
Interest  for  4  years  is  $  31.275  x  4  .     .     .     .        125.10 
Interest  for  7  months  is  J^  of  $  31.275  .     .     .  18.24 

Interest  for  20  days  is  |  of  j\,  or  ^\,  of  $  31.275  1.74 

Total $  145.08  ^ws. 

What  formula  applies  in  the  exercise  ? 
Explain  how  it  applies. 


172  INTEREST 

Written  Exercise  r.' 

175.  Find  the  interest  on  :  jt  ^*?V-' 

1.  $1500  for  2  years  4  months  10  days  at  8  %. 

2.  $635  for  1  year  3  months  2  days  at  7  %. 

3.  $955  for  3  years  6  months  15  days  at  6  %. 

4.  $2500  from  April  1,  1911,  to  July  1,  1914, 
a,t  8%. 

5.  $1450  from  March  5,  1910,  to  August  10, 
1913,  at  5  %. 

6.  $350.75  from  February  10,  1911,  to  January 
1,  1915,  at  51  %. 

Find  the  interest  and  the  amount : 

7.  $670  for  3  years  5  months  17  days  at  4  %. 

8.  $3000  from  Sept.  10,  1910,  to  Jan.  1,  1914, 
at  6  %. 

9.  $1850  from  May  20, 1908,  to  Oct.  10, 1911, 
at  5f  %. 

10.  $1725  from  Nov.  5,  1907,  to  Mar.  1,  1910, 
at  10  %. 

Six  Per  Cent  Method 

176.  The  plan  of  this  method  is  to  find  the  in- 
terest on  $  1  at  6  %  for  the  given  time  and  then 
to  multiply  this  sum  by  the  principal.  The  follow- 
ing values  are  of  practical  use  : 

The  interest  on  $  1  for  1  yr.  at  6  %  is  $  .06. 
The  interest  on  $  1  for  1  mo.  at  6  %  is  $  .005. 
The  interest  on  $  1  for  1  da.  at  6  %  is  $  .OOOj. 


SIX  PER  CENT  METHOD  173 

1.  Compute  the  interest  at  6  %  on  $  279.60  for 
3  years,  9  months,  24  days. 

Process  and  Explanation 

Interest  on  $  1  for  3  years  is  $.06  x  3      ...  $  .18 
Interest  on  $  1  for  9  montlis  is  $  .005  x  9    .     .      .045 
Interest  on  $  1  for  24  days  is  $  .000^  x  24  .     .      .004 
Interest  on  $  1  for  3  years,  9  months,  24  days     $  .229 
Hence  the  interest  on  $  279.60  for  3  years,  9  months,  24 
days  is  $  279.60  x  $.229  =  $  64.03.     Ans. 

What  formula   applies   here  ?     Explain   how  it    ^ 
applies.  T^ 

The  six  per  cent  method  may  be  used  for  finding 
the  interest  at  other  rates  by  taking  the  fractional 
part  the  required  rate  is  of  6  %  as  a  multiplier  of 
the  result  obtained  by  the  method. 

Written  Exercise 
177.  Find  the  interest  by  the  six  per  cent  method : 

1.  $  395  for  1  year  11  months  12  days  at  6  %. 

2.  $  914.50  for  3  years  6  months  18  days  at 
6%. 

3.  $732.25  from  Jan.  3,  1910,  to  Oct.  20, 
1913,  at  6  %. 

4.  $  1017.95  for  4  years   7  months  14  days  at 

6%. 

5.  $2180.60  from  Mar.  4,  1907,  to  Feb.  6, 
1913,  at  6  %. 


174  INTEREST 

6.  $  540  from  July  9,  1914,  to  Feb.  17,  1915, 
at  6%. 

7.  $  350  for  1  year  7  months  15  days  at  2  %. 

8.  $  715  for  2  years  2  months  28  days  at  4J  %. 

9.  $1576  from  Dec.  13,  1906,  to  April  10, 
1909,  at  5  %. 

10.  $  2935  from  Nov.  4,  1910,  to  Aug.  1,  1914, 

at  7  %  ? 

11.  $  1640.35  from  Oct.  25,  1911,  to  May  18, 
1914,  at  8%. 

12.  $  347  for  2  years  8  months  27  days  at  5^%. 

13.  $  1175  from  Sept.  30,  1904,  to  April  12, 
1907,  at  4  %. 

Written  Problems 

178.  1.  A  note  given  October  5,  1913,  for  $  654 
at  7  %  was  paid  December  23,  1915.  What  amount 
of  money  was  required  to  cancel  the  note  ? 

2.  A  bill  of  goods  amounting  to  $  5675  is  sold 
on  30  days'  time  or  at  a  discount  of  5  %  for  cash. 
Which  is  better  for  the  buyer  to  accept  if  money  is 
worth  8  %  ? 

3.  A  five-room  cottage  can  be  bought  for  $  2500 
or  rented  for  $  25  a  month.  Which  is  better,  to 
buy  or  rent,  if  money  is  worth  7  %  and  the  taxes, 
insurance,  and  up-keep  cost  $  65  a  year  ? 

4.  What  principal  at  6  %  will  produce  $  112 
interest  in  1  yr.  5  mo.  ? 


EXACT  INTEREST  METHOD  175 

5.  Find  the  principal  which  will  amount  to 
$  862.50  in  2  yr.  4  mo.  at  6  %. 

6.  At  what  rate  will  $480  yield  $  66.13  in  3  yr. 

5  mo.  10  da.  ? 

7.  In  what  time  will  $  490.92  yield  $  49.75  at 
8%? 

8.  A  bank  pays  S^  %  interest  on  a  deposit  of 
$  8000.     The  bank  loans  I  5000  for  3  months  at 

6  %  ;  all  of  it  for  4  months  at  5|  %  ;  and  again 
$  6000  for  5  months  at  5  % .  Does  the  bank  gain 
or  lose  and  how  much  ? 

Exact  Interest  Method 

179.  The  United  States  government  and  some 
banks  and  business  institutions  use  the  exact  inter- 
est method  of  computing  interest.  For  finding  the 
exact  time  between  two  dates  a  convenient  table 
is  often  used  in  banks  and  business  offices. 

This  method  takes  account  of  the  exact  number 
of  days  in  the  time  interval  and  proceeds  upon  the 
basis  of  365  days  to  the  year.  Thus :  2  years  122 
days  gives  2|-|-|  as  the  time  multiplier. 

Exact  interest  may  also  be  obtained  from  simple 
interest.  Thus  :  by  simple  interest  1  day's  interest 
is  -g^Q-  of  a  year's  interest,  and  by  exact  interest  1 
day's  interest  is  -g^  of  the  interest  for  a  year. 
The  difference  between  g-l^  and  -3  Jj  is  ^.  That 
is,  the  exact  interest  is  ^  less  than  the  simple 
interest. 


176  INTEREST 

Process  and  Explanation 
1.    What  is  the  exact  interest  on   $  632.96  for 
240  days  at  6  %  ? 

(a)  Interest  for  one  year  is  $  632.96  x  .06  =  $  37.98. 
Interest  for  ffl  of  a  year  is  |||  x  $  37.98  =  $24.97. 
(6)  240  days  is  ||^  or  |  of  a  year.     Hence  the  simple 
interest  for  240  days  is  |  of  $  37.98  =  $  25.32. 
j\  of  $  25.32  =  %  .35. 
$  25.32  —  $.35  =  $  24.97,  the  exact  interest.     Ans. 

Written  Exercise 

180.  Find  the  exact  interest : 

1.  $  860  for  1  year  4  months  17  days  at  7  %. 

2.  $  1345  for  2  years  9  months  23  days  at  6  %. 

3.  $  2631.50  from  Mar.   19,  1914,  to   Sept.  3, 
1915,  at  51  %. 

4.  $  1930  from  Oct.  6,  1909,  to  June  10,  1914, 
at  8%. 

5.  $  640.80  from  March  15,  1915,  to  June  24, 
1915,  at  6  %. 

6.  $  1254.25  from  June  24,  1915,  to  Sept.  18, 

1915,  at  7  %. 

7.  S  4872.80  from  May  17,   1915,  to  Dec.  27, 

1916,  at  8  %. 

8.  $  2958  from  Sept.  28,  1915,  to  Jan.  6,  1916, 

at  61%. 

Written  Problems 

181.  1.    What  is  the  difference  between  simple 
and  exact  interest  on  $  7650  for  154  days  at  6  %? 


COMPOUND  INTEREST  METHOD  177 

2.  A  banker  borrowed  $  15,000  in  Illinois  at 
5  %  exact  interest,  and  loaned  it  in  Nebraska  at 
8  %  simple  interest.  What  was  his  profit  in  185 
days? 

3.  A  man  bought  a  farm  for  $  8000.  He  paid 
$  1600  cash  and  $  800  a  year  thereafter  until  it 
was  paid  for.  With  money  worth  6  %  what  was 
the  total  amount  paid  for  the  farm  ?  Get  the 
interest  by  both  methods  and  find  the  difference 
between  them. 

4.  A  farmer  bought  a  horse  for  $  250.  He  paid 
$  60  cash.  Which  is  the  better  proposition  for 
him,  to  borrow  the  rest  at  the  bank  at  6  %  exact 
interest,  or  give  his  note  at  simple  interest  at  5|-  % 
for  240  days  ? 

5.  A  note  for  $  1250  dated  July  28,  1914,  at 
8  %  had  the  following  indorsements :    August    8, 

1914,  $  50 ;  December  5,  1914,  $  50  ;  January  9, 

1915,  $  50  ;  February  3, 1915,  $  50  ;  April  5,  1915, 
$  50.  If  the  interest  stopped  on  the  amount  paid 
at  the  time  of  each  payment,  what  was  due  July 
28,1915? 

COMPOUND   INTEREST 

182.  If  when  the  interest  falls  due  it  is  added 
to  the  principal  and  the  amount  forms  a  new 
principal  which  draws  interest,  the  interest  is  said 
to  be  compounded  and  is  called  compound  interest. 


178  INTEREST 

The  interest  may  be  compounded  quarterly,  semi- 
annually, or  annually.  Compound  interest  is  allowed 
on  deposits  in  savings  banks.  It  is  also  used  by 
business  men  in  finding  the  cumulative  value  of 
investments  at  a  given  rate,  where  the  earnings 
are  not  withdrawn. 

1.    Find  the  compound  interest  and  amount  on 
$200   for   3   years  at    7%,  interest   compounded 

annually. 

Process  and  Explanation 

$  200  is  the  first  principal. 

$  200  X  .07  =  $  14,  first  interest. 

$  200  +  $  14  =  $  214,  the  second  principal. 

$  214  X  .07  =  $  14,98,  second  interest. 

$  214  +  $  14.98  =  $  228.98,  third  principal. 

$  228.98  X  .07  =  $  16.0286,  third  interest. 

$  228.98  +  $  16.03  =  $  245.01,  amount  at  the  end  of   the 
third  year. 

Hence,  $  245.01  —  $  200  =  $  45.01,  compound  interest  for 
3  years.    Arts. 

Written  Exercise 

183.    Find  the  compound  interest  on  : 

1.    $265  for  3  years  at  4%. 

•     2.    $  2400  for  4  years  at  6  %. 

3.  $3650  for  3  years  at  5%. 

4.  $  1925  for  5  years  at  8  %. 

5.  $  4270  for  4  years  at  7  %. 

Find  the  amount  and  interest  compounded  semi- 
annually : 

6.  $  300  for  1  year  6  months  at  5  %. 


WRITTEN  PROBLEMS  179 

7.  $  1250  for  1  year  9  months  at  6 %. 

8.  $  4950  for  3  years  at  5  %. 

9.  $6200  from  July  1,  1909,  to  Nov.  25,  1912, 
at  4%. 

Written  Problems 

184.  1.  A  boy  on  his  ninth  birthday  has  $  300 
deposited  for  him  in  a  savings  bank.  If  the  bank 
pays  4  %  interest  compounded  semiannually,  what 
amount  will  he  have  to  his  credit  wh^n  he  is 
21  years  of  age  ? 

2.  A  man  deposited  $  1750  in  a  savings  bank, 
which  pays  4  %  semiannually,  for  3  years.     Com- 
pare the  amount  with  tha,t  resulting  from  a  simple 
interest  loan  of  the  same  principal   for  the  same  - 
time  at  5  % . 

3.  A  father  on  his  son's  twelfth  birthday  de- 
posited $  15.  If  he  deposits  $  15  every  six  months 
thereafter  until  the  son  is  21,  bow  much  will  he 
have  to  his  credit  if  the  bank  pays  4  %,  com^ 
pounded  semiannually  ? 

4.  What  sum  deposited  at  4  %  interest,  com- 
pounded annually,  will  amount  to  $  1000  in 
30  years? 

5.  A  man  deposited  $  1375  in  a  savings  bank,  • 
which  pays  3%  interest  compounded  semiannually, 
for  five  years.     Compare  the  amount  with  that  re- 
sulting from  a  simple  interest  loan  of  the   same 
principal  for  the  same  time  at  41%. 


BUSINESS   PAPERS 

NOTES 

185,  A  note  is  a  written  promise  to  pay  a  cer- 
tain sum  of  money  at  a  specified  time.  The  fol- 
lowing is  the  usual  form  of  a  note : 


^  75.00  Manhattan,  Kansas,  foyn.  30,  1916. 

€.n,t  i^s^cM,  after  date J.... promise  to  pay  to 

^ta/\A  o{'tam,t&u, or  order^ 

Value  Received,  with  interest  at  6%. 


The  payment  of  a  note  is  often  made  more  se- 
cure by  the  signatures  of  other  persons,  known  as 
indorsers,  or  by  a  conveyance  of  property,  real  or 
personal,  in  case  the  note  is  not  paid.  When  prop- 
erty is  designated  as  security,  the  instrument  of 
conveyance  is  called  a  mortgage.  Mortgages  are 
of  two  kinds :  chattel,  or  a  mortgage  on  personal 
property,  and  a  real  estate  mortgage  deed.  In 
either  case  the  owner  *  retains  possession  of  the 
property  until,  upon  non-payment  of  the  note,  legal 
proceedings  known  as  foreclosure  require  that  the 
property  be  turned  over  to  satisfy  the  claim. 

180 


CHECKS 


181 


Indorsement  in  Blank. 


•S'oA.i  to-  tk&  cyvct&v  ai- 
S'k&  TVla/yikaXZa.'yi  Bo/nk,. 
^toA^k,  ofta/yileA^ 

Indobsement  in  Full. 


The  indorsement  may  appear  on  the  back  of  the 
note  as  follows : 

In  the  first  two  of 
these  indorsements  Clark 
Stanley  guarantees  the 
payment  of  the  note.  If 
Clark  Stanley  does  not 
wish  to  become  respon- 
sible for  the  payment  of 
the  note  in  case  Dudley 
Stanton  fails  to  pay  it 
when  due,  he  may  indorse 
the  note  without  recourse  as  indicated  in  the  third  in- 
dorsement. 

CHECKS 

186.  Money  on  deposit  in  a  bank  in  an  open 
account  is  subject  to  check;  i.e.,  the  bank  will  pay 
any  part  or  all  of  it  upon  a  written  order  from  the 
depositor,  called  a  check.  The  check  is  usually  in 
the  following  form : 


JVb.  00  Manhattan,  Kansas,  jam,.  30,  1916 

Ete  JHantattan  Bank 

Manhattan,  Kansas 
Toy  to ^ta^vk  cfUi-yvt&j or  order 

ofev-e'yityu—yi'i'yi&  cuyvct  —'rT-c-cccr:^crryr:rrrTcr: Dollars. 

'  100 

/  r9§^  ^udCay  ^tciyitcyyi. 


182 


BUSINESS  PAPERS 


A  check  is  usually  made  payable  to  a  person  or 
to  his  order.  When  the  check  has  been  paid  it  is 
finally  returned  to  the  maker,  or  the  depositor,  who 
signed  the  check.  A  depositor  wishing  to  with- 
draw money  makes  the  check  payable  to  "  self." 
If  a  depositor  wishes  to  send  money  away  to  a 
stranger,  it  is  desirable  to  have  the  check  show 
that  it  has  actual  value.  To  do  this  the  maker 
takes  it  to  the  bank  upon  which  it  is  drawn  and 
has  the  cashier  write  across  the  face  and  over  his 
signature  the  words  "  good  when  properly  in- 
dorsed." This  makes  what  is  called  a  certified 
check.  The  bank  simply  sets  aside  enough  from 
the  depositor's  account  to  pay  the  check  and  will 

not  release  that  amount 
until  the  check  has  been 
returned. 

When  one  wishes  to 
cash  a  check  he  writes 
his  name  on  the  back,  or 
in  other  words  he  in- 
dorses the  check,  and 
presents  it  for  payment. 
When  one  wishes  to  sell 
a  check  that  has  been 
made  payable  to  him,  he 
may  do  so  by  indorsing  it;  and  the  person  to  whom 
he  has  sold  it  will  then  be  able  to  collect  the  face 
of  the  note  by  indorsing  it  and  then  presenting  it 


tcivk>  ^'tuntan. 


Inoobsement  in  Blank. 


Indorsement  foe  Deposit. 


S'O'if  to  jakn  SC&td. 

Indorsement  in  Full. 


NOTES  183 

to  the  bank  for  payment.     The  indorsement  on  the 
check  will  appear  as  on  the  opposite  page. 

Money  may  be  deposited  in  a  dosed  account,  — • 
one  that  is  not  subject  to  check.  In  such  cases, 
the  bank  may  issue  a  certificate  of  deposit,  which 
certifies  the  amount  that  will  be  paid  to  the  de- 
positor when  the  certificate  is  returned  properly  in- 
dorsed. This  may  be  a  demand  or  a  time  certificate. 
Time  certificates  usually  draw  interest. 

Written  Exercise 

187.  1.  Write  a  note  for  $  350  payable  to  some 
member  of  the  class  for  90  days  at  6%.  Deter- 
mine the  interest  and  amount. 

2.  A  note  was  given  at  Topeka,  Kansas,  Janu- 
ary 29, 1915,  by  A.  G.  Hunting  to  H.  R.  Sunderland 
for  %  128.50,  to  run  60  days  at  7  %.  Write  the  note 
up  in  the  proper  form  indicating  that  P.  T.  Small 
was  a  security  for  its  payment.  Determine  the 
interest  and  amount  of  the  note. 

3.  Mr.  C.  F.  Garland,  Peoria,  Illinois,  borrowed 
$212.50,  February  16,  1916,  at  6%  for  1  year 
from  J.  H.  Chamberlain.  Make  out  the  note  in  the 
proper  form  indicating  that  B.  R.  Carter  was  a 
security  for  its  payment.  Find  the  interest  and 
amount  due  at  the  end  of  the  year. 

4.  Secure  blank  checks,  and  have  the  pupils 
write  checks  to  each  other  until  they  are  familiar 
with  the  proper  forms. 


POWERS   AND   ROOTS 


5 


POWERS 

188.  The  square  in  the  accompanying  figure  evi- 
dently has  5  units  on  each  side  and  an  area  of  25 
square  units.  Hence,  25  is  called 
the  square  of  5.  In  general  we 
have  the  definition:  The  square 
of  a  number  is  the  product  of  the 
number  taken 
twice  as  a  fac- 
tor. 
The  cube  in  the  figure  here 
has  3  units  on  each  edge  and  a 
volume  of  27  cubic  units.  Hence, 
27  is  called  the  cube  of  3.  The 
cube  of  a  number  is  the  product  of  the  number 
taken  3  times  as  a  factor. 

Squares  and  cubes  are  special  cases  of  powers 
of  numbers.  Taking  a  number  two  times  as  a 
factor  gives  the  second  power ;  three  times  as  a 
factor  the  third  power ;  four  times  as  a  factor  the 
fourth  power,  etc. 

Instead  of  writing  at  length  4x4x4x4x4  we 
may  use  the  simpler  form  of  4^  Hence  4  is  called 
the  base  and  5  the  exponent.     The  exponent  of  a 

184 


y 

^    ^    ^  A 

y    /    A\ 

X    y    / 

/ 

/ 
/ 

/ 
/ 
/ 

/ 
/ 

/ 

V 

POWERS  185 

power  is  a  number  placed  to  the  right  and  above 

the  base  to  indicate  how  many  times  the  base  is 
taken  as  a  factor. 

Written  Exercise 
189.   Find  the  value  of : 

1.  28^          4.    1.53           7.    64  10.    4262 

2.  113               5,     (1)2               8.     28  11.     3.73 

3.  1162           6.     (1)3               9.      (lf)5  12.     .9^ 


H 


Often  the  square  of  a  number  can  be  found  more 
readily  by  use  of  a  formula  than  by  the  regular 
method  of  multiplication.  The  truth  of  the  fol- 
lowing rule  is  illustrated  by  the  adjoining  figure. 

The  illustration  shows  the  square  of  43 ;  43^  = 
(40  +  3)2  =  402  +  2x40x3  +  32=1600  +  240  +  9  = 
1849.  The  method  here  given 
can  be  used  with  any  two  num- 
bers. 

Representing  any  two  numbers 
by  the  lines  m  and  w,  we  see  that 
the  square  of  their  sum  involves 
two  squares  m  and  n,  and  two 
rectangles  mn.  Hence,  the  following  rule :  The 
square  of  the  sum  of  two  numbers  equals  the 
square  of  the  first  plus  twice  the  product  of  the 
first  and  second,  plus  the  square  of  the  second. 
Or  in  letters,  the  formula  : 

Formula :        (m  +  71)2  =  m2  +  2  mn  +  ^2. 


40x3 

3^ 

40^ 

CO 

Xi 

0 

186  POWERS  AND  ROOTS 

Written  Exercise 

190.  Use  the  formula  to  find  the  squares. 

1.  41  5.  93  9.  105  13.  327  iv.  253 

2.  27  6.  86  10.  91  14.  214  is.  79 

3.  35  7.  82  11.  59  15.  47  i9.  416 

4.  68  8.  75  12.  123  16.  96  20.  425 

Written  Problems 

191.  1.  A  fence  surrounding  a  square  field  has 
an  entire  length  of  320  rods.  How  many  acres  in 
the  field  ? 

2.  A  square  court  is  to  be  paved  with  Belgian 
blocks,  each  block  being  an  eight-inch  cube.  If 
the  court  is  8  rods  square,  how  many  blocks  will 
be  required  ? 

3.  A  cubical  tank  is  10  feet  8  inches  on  a  side, 
inside  measurements.  How  many  gallons  will  it 
hold? 

4.  What  will  it  cost  to  line  an  open  tank  which 
is  12  feet  4  inches  long,  4  feet  5  inches  wide,  and  3 
feet  deep,  at  9 J  ^  a  square  foot  ? 

5.  The  pedestal  of  a  monument  is  a  cube  of 
granite  3  feet  4  inches  on  a  side.  What  is  its 
volume  ? 

6.  The  length  of  a  side  of  the  square  base  of  the 
great  Pyramid  of  Cheops  is  approximately  45  rods 
10  feet.     How  many  acres  does  the  base  cover? 


ROOTS  187 


ROOTS 


192.  If  36  be  written  as  the  product  of  two 
equal  factors  6  and  6,  that  is,  36  =  6x6,  then  one 
of  these  factors  is  called  the  square  root  of  36. 
The  square  root  of  a  number  is  one  of  the  two 
equal  factors  of  the  number.  Similarly,  if  we 
write  125  as  5  X  5  X  5,  then  one  of  these  factors  is 
called  the  cube  root  of  125.  The  cube  root  of  a 
number  is  one  of  the  three  equal  factors  of  the 
number. 

The  sign  ^,  called  the  radical  sign,  is'  used  to 
indicate  the  root  of  a  number.  To  show  what  root 
is  to  be  taken,  a  figure  called  the  index  of  the 
root  is  placed  in  the  opening  of  the  radical  sign. 
Thus  -y/27  indicates  the  cube  root  of  27.  When 
no  index  is  written,  the  square  root  is  meant. 

Since  12  =  1,  10^  =  100,  100^  =  10,000,  etc.,  where 
do  the  square  roots  of  all  the  numbers  between  1 
and  100  lie  ?    between  100  and  10,000  ? 

If  a  whole  number  be  divided  into  groups  of 
two  figures  each  from  the  right  to  the  left,  the 
number  of  groups  will  equal  the  number  of  figures 
in  the  root. 

Since  raising  to  the  second  power  and  extracting 
the  square  root  are  opposite  processes,  compare  the 
process  of  extracting  the  square  root  with  the  pro- 
cess of  squaring  a  number. 

1.   Extract  the  square  root  of  1849. 


188  POWERS  AND  ROOTS 

Process  Explanation :  The  two  groups  found 

1849  (40  4-3       on  separating  the  number  into  periods 
XQOQ  show  that  the  root  contains  2  figures. 

83   249  The  first  group  of  figures,  "  18  ",  con- 

249  tains  the  square  of  the  tens  number  of 

the  root.  The  greatest  square  in  18  is 
16 ;  and  the  square  root  of  16  is  4  (40  units).  Four  is  there- 
fore the  tens  figure  in  the  root.  Subtracting  the  square  of 
the  tens  from  1849,  we  have  the  remainder  249.  This  must 
contain  two  times  the  tens,  times  the  units  plus  the  units 
squared.  Twice  the  4  tens  is  8  tens.  Eight  is  contained  in 
24  tens  3  times.  We  therefore  try  3  as  the  next  figure  of 
the  root.  Now  the  remainder  may  be  written  in  the  form 
(twice  the  tens  plus  the  units)  times  the  units.  Hence,  the 
quantity  in  the  parenthesis  is  to  be  used  as  the  divisor  in  the 
final  determination  of  the  unit  figure  of  the  root.  Therefore, 
in  the  example  we  have  (80  plus  3)  times  3,  which  gives  249. 
Hence,  43  is  the  required  square  root  of  1849. 

In  practice  the  work  is  shortened  by  the  omis- 
sion of  unnecessary  zeros  as  follows  : 

1849  (43 
16 
83 


249 
249 


Rule  for  the  extraction  of  square  root :  Begin  at 
the  decimal  point  and  separate  the  number  into  groups 
of  two  figures  each,  to  the  left  for  the  integral  part 
and  to  the  right  for  the  decimal  part  of  the  number. 

Find  the  greatest  square  in  the  left  period,  and 
write  down  its  square  root  as  the  first  figure  in  the 
required  i^esult. 


SOLUTION  OF  THE  RIGHT  TRIANGLE        189 

Subtract  the  square  of  this  root  figure  from  the 
first  period,  and  bring  doivn  the  next  period.  Double 
the  part  of  the  root  already  found  (regarded  as  tens) 
for  a  trial  divisor,  divide  it  into  the  remainder,  and 
write  the  i7iteg7^al  part  of  the  quotient  as  the  next 
figure  of  the  root. 

Add  to  the  trial  divisor  the  root  figure  just  found 
to  make  the  complete  divisor,  multiply  this  result  by 
the  last  root  figure,  and  subtract  the  product  from 
the  last  remainder. 

Bring  down  the  next  ^^eriod,  and  proceed  as  before 
until  the  desired  number  of  figures  of  the  root  have 
been  found. 

Written  Exercise 

193.    Extract  the  square  root  of  the  following: 

1.  109,561.       7.  .0000064.       i3.  2.3  to  3  places. 

2.  4,198,401.    8.  1,027.8436.    i4.  78.15 to  3  places. 

3. 

4. 


6. 


The  Solution  of  the  Right  Triangle 
194.    The  square  on  the  hypotenuse  of  a  right 
triangle  equals  the  sum  of  the  squares  on  the  other 
two  sides. 


64 
361- 

9. 

.00267289. 

15.  219  to  4  places. 

.7329. 

10. 

169 
676- 

16.  165  to  4  places. 

18.9225. 

11. 

40,195,600. 

17.    47  to  4  places. 

366,025. 

12. 

7  to  3  places. 

18.    1  to  4  places. 

19.    381  to  4 

places.     20. 

905  to  4  places. 

190 


POWERS  AND  ROOTS 


For  example  :  if  ^C  =  18  and  ^C  =  24,  find  the 
length  of  AB.  AB^  =  AC^ -\- BCK  Why?  Or 
J.^  =  182  +  242=  324  +  576  =  900,  ^j.  j^^^  ^q 

From    the    geometric 
facts  stated  in  the  pre' 


ceding    paragraph,    the 
square  on  either  side  of 

a  right  triangle  equals  the  difference  ^a 

of  what  squares  ? 

If  ^^  =  20,  and  AC=  16,  find  BC.        20 


Written  Problems 


16 
C 


195.  1.  A  square  field  contains  10  acres.  How 
many  rods  of  fence  will  it  take  to  inclose  it  ? 

2.  Two  sides  of  a  right  triangle  are  65  and  74 
feet.  Find  to  three  decimal  places  the  length  of 
the  hypotenuse. 

3.  The  hypotenuse  of  a  right  triangle  is  94  feet. 
One  side  is  43  feet.  Find  the  length  of  the  other 
side  to  three  decimal  places. 

4.  A  rope  314  feet  long  is  stretched  from  the  top 
of  a  flagpole    100    feet   high.     Find  the  distance 


WRITTEN  PROBLEMS  191 

from  the  base  of  the  pole  to  the  point  of  contact 
of  the  rope  with  the  ground. 

5.  A  pasture  in  the  shape  of  a  right  triangle 
is  120  rods  4  yards  and  69  rods  3  yards  on  the 
sides  about  the  right  angle.  Find  the  length  of 
the  hypotenuse. 

6.  A  room  is  18  by  14  by  10  feet.  How  far  is 
it  from  a  floor  corner  to  the  diagonally  opposite 
ceiling  corner  ? 

7.  Find  the  diagonal  of  a  rectangular  field  120 
by  80  rods. 

8.  A  baseball  diamond  is  90  feet  on  a  side. 
Find  the  distance  from  the  second  base  to  the  home 
plate. 

9.  If  there  are  250  shingles  in  a  bunch,  averag- 
ing 4  inches  in  width,  how  large  a  square  of  roof 
will  8  bunches  cover  if  laid  4  inches  to  the  weather  ? 

10.  A  cubical  box,  open  at  the  top,  has  a  surface  of 
79,380  square  inches.     Find  its  dimensions  in  feet. 

11.  A  cylindrical  grain  bin  12  feet  deep  will  hold 
1500  bushels  of  wheat.     What  is  its  diameter? 

12.  A  tree  broken  42  feet  from  the  ground  re- 
mains fastened  to  the  stump.  If  the  top  reaches  the 
ground  54  feet  from  the  stump,  what  was  the  height 
of  the  tree  before  it  was  broken  ? 

13.  A  30-foot  silo  holds  196  tons.  What  is  its 
diameter  if  one  cubic  foot  of  silage  weighs  39.6 
pounds  ? 


RATIO  AND  PROPORTION 
RATIO 

Study  Exercise 

196.   The  ratio  of  two  quantities  of  the  same  kind 

is  their  relation  as  expressed  by  division;  thus  |,  f 
are  ratios.  Another  way  of  writing  such  ratios  is 
the  following :  2:5;  3:7,  which  are  read  2  is  to 
5,  3  is  to  7.  Hence,  the  ratio  relation  between  two 
numbers,  written  in  either  form,  is  an  indicated 
division. 

The  two  elements  of  a  ratio  are  called  its  terms. 
The  antecedent  is  the  first  term,  and  the  consequent 
is  the  second.  The  ratio  itself  is  always  an  abstract 
number.  Since  a  ratio  is  really  a  fraction,  all  the 
rules  concerning  the  operations  of  fractions  will 
hold  here.  In  particular  we  note  that  multiplying 
or  dividing  both  terms  of  a  ratio  by  the  same  num- 
ber does  not  change  its  value. 

Often  in  a  statement  that  contains  two  or  more 
numbers,  a  clearer  idea  of  their  relation  can  be  had 
by  taking  some  one  of  the  numbers  as  a  unit  of 
comparison.  Thus :  4  :  24  is  the  same  as  1 :  6. 
Similarly,  by  using  a  series  of  ratio  signs  we  may 
compare  a  set  of  numbers  like  6,  18,  36  by  use  of 

192 


RATIO  193 

the  form  1:3:6.  The  principle  involved  is  that 
of  dividing  the  terms  of  the  ratio  by  the  same 
number  without  a  change  of  value. 

Oral  Exercise 

197.  1.    Find  the  number  whose  ratio  to  3  is  4. 

2.  Find  the  number  whose  ratio  to  8  is  5. 

3.  What  is  the  number  to  which  30  has  the 
ratio  5  ? 

4.  What  is  the  number  to  which  42  has  the 
ratio  6  ? 

5.  The  ratio  of  the  height  of  a  tree  to  that  of  a 
post  is  7|.  The  post  is  6  feet  high.  How  high  is 
the  tree  ? 

6.  The  ratio  of  the  length  of  a  crib  to  its  width 
is  3J.     If  the  crib  is  35  feet  long,  how  wide  is  it  ? 

7.  Separate  15  into  the  ratio  of  2  to  1. 

8.  Separate  20  into  the  ratio  of  3  to  2. 

9.  Counting  the  school  days  in  a  week  and  4 
weeks  in  a  month,  what  is  the  ratio  of  the  number 
of  school  days  to  the  average  number  of  days  in  a 
month  ? 

Written  Exercise 

198.  Reduce  each  of  the  following  to  a  ratio 
having  one  for  its  first  term : 

1.  7:14.  3.    17:68.  5.    60:320. 

2.  11:33.  4.    14:30.  6.    9:108. 


194  RATIO  AND  PROPORTION 

7.  28  ft. :  142  ft.     9.   .1  oz. :  f  oz.    ii.   .512  :  8. 

8.  19  lb.  :  65  lb.    10.  f :  40.  12.  .78  ft. :  17  in. 

Express  the  following  sets  of  numbers  by  a  series 
of  ratios  having  one  for  the  tirst  term : 

13.  9:27:72.  15.    5:19:26. 

14.  7:98:84.  16.   f:|:ll. 


Written  Problems 

199.  1.  In  an  experiment  in  alfalfa  breeding  6.3  % 
of  the  plants  of  the  American  and  39.3  %  of  those 
of  the  Turkestan  variety  withstood  a  hard  frost 
without  injury.  Determine  the  comparative  frost- 
resisting  powers  of  the  two  varieties  in  the  form 
of  a  ratio  having  one  for  the  first  term. 

2.  The  sunshine  record  in  the  neighborhood  of 
St.  Paul,  Minn.,  for  1911  shows  the  presence  of 
sunshiny  days  for  |-  of  the  time  during  the  spring 
and  summer  months,  and  for  J  of  the  time  during 
the  fall  and  winter  months.  Find  the  ratio  of  the 
sunshiny  days  to  the  cloudy  days  during  the  year. 

3.  In  1910  the  enrollment  of  students  in  the 
colleges  of  agriculture  and  mechanic  arts  of  the 
United  States  in  residence  courses,  was  45,000 ;  in 
correspondence  courses;  30,000 ;  and  in  extension 
courses,  21,000.  Compare  these  numbers  in  the 
form  of  a  ratio,  taking  the  number  in  the  exten- 
sion courses  as  one. 


PRACTICAL    APPLICATIONS  195 

4.  In  1912  the  values  of  the  four  principal 
crops  of  the  United  States  in  millions  of  dollars 
were  as  follows:  corn,  1759;  hay,  861;  cotton, 
735 ;  wheat,  596.  Compare  these  values  in  the 
form  of  a  ratio,  using  the  value  of  wheat  as  the 
basis  of  comparison. 

5.  In  a  germination  experiment  with  wheat  in 
1909,  97  %  of  the  kernels  of  greater  density  ger- 
minated, and  71  %  of  the  kernels  of  lesser  density 
germinated.     Express  these  results  in  ratio  form. 

6.  According  to  the  census  of  1907,  the  popu- 
lation per  square  mile  on  the  great  continents  is 
as  follows :  Europe,  106 ;  Asia,  58  ;  Africa,  11 ; 
America,  9.  Write  these  results  in  the  form  of  a 
ratio  series,  with  the  population  of  America  as  the 
unit  of  comparison. 

7.  The  average  yield  of  wheat  in  bushels  per 
acre  of  the  chief  wheat-producing  nations  of  the 
world  in  1912  was :  United  States,  15.9 ;  Russia, 
10.2 ;  Germany,  33.7  ;  Austria,  22.4  ;  France,  20.4 ; 
Great  Britain,  31.7.  Determine  the  comparative 
yield  per  acre  of  these  countries,  taking  the  United 
States  yield  as  unity. 

PRACTICAL  APPLICATIONS 

(1)    SPECIFIC    GRAVITY 

200.  The  specific  gravity  of  a  substance  is  the 
ratio  of  its  weight  to  the  weight  of  an  equal  volume 


196  RATIO  AND  PROPORTION 

of  water.  It  is  known  that  one  cubic  foot  of  pure 
water  weighs  nearly  62.5  pounds.  Hence,  the 
specific  gravity  of  any  substance  may  be  found 
directly  when  its  weight  per  cubic  foot  is  known, 
or  the  weight  per  cubic  foot  can  be  found  when 
the  specific  gravity  is  given. 

Written  Exercise 
201.   Find  the  specific  gravity  of  the  following 
substances  whose  weight  per  cubic  foot  is  given : 

1.  Cast  iron,  450  pounds.  5.    Ice,  57.5  pounds. 

2.  Wrought  iron,  480  pounds.       6.   Cork,  15  pounds. 

3.  Steel,  490  pounds.  7.    Butter,  58.7  pounds. 

4.  Copper,  552  pounds.  8.    Marble,  168.7  pounds. 

Find  the  weight  per  cubic  foot  of  the  following 
substances  whose  specific  gravities  are  given : 


9. 

Lead,  11.418. 

19. 

Poplar,  .48. 

10. 

Silver,  10.5. 

20. 

White  oak,  .77. 

11. 

Gold,  19.5. 

21. 

Milk,  1.03. 

12. 

Tin,  7.291. 

22. 

Alcohol,  .79. 

13. 

Mercury,  13.596. 

23. 

Linseed  oil,  .94. 

14. 

Brick,  common,  1.79. 

24. 

Turpentine,  .99. 

15. 

Brick,  pressed,  2.16, 

25. 

Sulphur,  2.04. 

16. 

Hickory,  .77. 

26. 

Lime,  .804. 

17. 

White  pine,  .45. 

27. 

Salt,  2.13. 

18. 

Yellow  pine,  .61. 

Written  Problems 
202.   1.    How  many  tons  of  ice  may  be  harvested 
from  a  section  of  a  pond  128  feet  by  320  feet  if 
the  ice  is  8J-  inches  deep  ? 


PRACTICAL  APPLICATIONS  197 

2.  Find  the  weight  of  a  cubic  meter  of  lead,  in 
pounds ;  in  kilograms. 

3.  How  high  must  a  column  of  mercury  be  to 
cause  a  pressure  16.4  pounds  per  square  inch  ? 

4.  If  50  cubic  inches  of  a  substance  weigh  8 
pounds,  what  is  its  specific  gravity  ? 

5.  Find  the  weight  of  a  marble  shaft  8  feet 
high  and  having  a  uniform  cross  section  of  2  feet 
by  2  feet  6  inches. 

(2)    RATIONS 

203.  A  matter  of  importance  to  every  farmer  in 
handling  his  stock  is  that  of  feeding.  The  ques- 
tion of  how  to  make  feeds  yield  the  most  in  ani- 
mal products  is  ever  before  him.  The  problem  is 
a  complex  one,  and  the  exact  solution  of  it  is  not 
known.  Much  has  been  done,  however,  in  ascer- 
taining the  combination  of  feeds  best  adapted  for 
a  given  purpose  with  different  animals  under  given 
conditions.  The  results  of  experiments  along  this 
line  have  been  embodied  in  a  table  of  feeding 
standards  which  may  well  be  used  as  a  practical 
guide  to  feeders. 

A  ration  is  the  amount  of  feed  given  to  an  ani- 
mal during  24  hours. 

A  balanced  ration  is  one  which  contains  the 
various  nutritive  elements  in  such  amounts  as  best 
to  serve  the  purpose  for  which  the  animal  is  being 
fed. 


198 


RATIO  AND  PROPORTION 


Since  the  value  of  a  given  feed  depends  for  pro- 
duction purposes  upon  the  amounts  of  digestible 
nutrients  it  contains,  a  convenient  table  giving 
such  information  with  respect  to  the  common 
feeds  used  for  farm  animals  is  inserted  here. 


Table  of  Digestible  Nutrients  in  Certain  Feeds 


Fbeds 

Per  cent  op 

Per  cent  op 

Per  cent  of 

PUOTEIN 

Carbohydrates 

Fats 

Corn 

7.14 

66.12 

4.97 

Kafir     .... 

. 

5.78 

53.58 

1.33 

Corn  stover  .     . 

1.98 

33.16 

0.57 

Corn  silage    .     . 

1.21 

14.56 

0.88 

Corn  meal     .     . 

6.26 

65.26 

3.5 

Corn-and-cob  meal 

4.76 

60.06 

2.94 

Oats      .... 

9.25 

48.34 

4.18 

Wheat  bran  .     . 

12.01 

41.23 

2.87 

Wheat  middlings 

12.79 

53.15 

3.4 

Cottonseed  meal 

37.01 

16.52 

12.58 

Timothy  hay 

2.89 

43.72 

1.43 

Alfalfa  hay   . 

13.24 

39.26 

0.89 

Red  clover  hay 

7.38 

38.15 

1.81 

Prairie  hay    . 

0.61 

46.9 

1.97 

Cowpea  hay  . 

10.79 

38.4 

1.51 

Soybean  hay . 

10.78 

38.72 

1.54 

Whole  milk  . 

3.38 

4.8 

3.7 

Skim  milk     . 

3.01 

5.1 

0.3 

Linseed  meal 

28.76 

32.81 

7.06 

Shorts  .     .     . 

16.9 

62.4 

5,1 

The  following  table  of  feeding  standards,  show- 
ing the  amounts  of  nutrients  required  per  day  for 
1000  pounds  live  weight,  is  the  one  in  largest  use. 
Any  such  table  should  be  taken  as  a  useful  guide 


PRACTICAL  APPLICATIONS 


199 


to  be  modified  in  accordance  with  available  feeds, 
market  prices,  and  other  conditions  : 

Table  of  Feeding  Standards 
(Selected  from  Wolf-Lehman  tables) 


Animal 

Digestible  Nutrients 

Protein 

Carbohydrates 

Fats 

Horse  (heavy  work) 

Horse  (light  work) 

Fattening  cattle  (first  period)     . 
Fattening  cattle  (second  period) 
Fattening  cattle  (third  period)  . 
Dairy  cow  (16|  lb.  milk  daily)     . 
Dairy  cow  (22  lb.  milk  daily) 
Fattening  swine  (first  period)     . 
Fattening  swine  (second  period) 
Fattening  swine  (third  period)   . 
Fattening  sheep  (first  period)     . 
Fattening  sheep  (second  period) 
Growing  cattle  (6  to  12  mo.  old) 
Growing  swine  (3  to  5  mo.  old)  . 

2.5 
1..5 
2.5 

3.0 
2.7 
2.0 
2.5 
4.5 
4.0 
2.7 
3.0 
3.5 
2.5 
5.0 

13.3 
9.5 
15.0 
14.5 
15.0 
11.0 
13.0 
25.0 
24.0 
18.0 
15.0 
14.5 
13.2 
23.1 

0.8 

0.4 
0.5 
0.7 
0.7 
0.4 
0.5 
0.7 
0.5 
0.4 
0.5 
0.6 
0.7 
0.8 

In  comparing  a  given  ration  with  one  meeting 
the  requirements  of  the  feeding  standards,  use 
must  be  made  of  the  per  cent  table  of  nutrients  in 
order  to  determine  their  amounts  in  pounds  in  the 
ration. 

The  comparative  costs  of  different  rations  in- 
tended to  serve  the  same  purpose,  can  of  course  be 
found  if  the  prices  of  feeds  are  known.  Pupils 
should  make  a  local  price  list  of  the  common  feeds 
for  the  class  use. 


200  RATIO  AND  PROPORTION 

Oral  Exercise 

204.  1.  How  many  pounds  each  of  the  digestible 
•nutrients  in  100  pounds  of  corn  ?     In  500  pounds  ? 

2.  What  is  the  total  amount  of  digestible  nu- 
trients in  100  pounds  of  corn  ?     In  500  pounds  ? 

3.  How  many  pounds  of  each  of  the  digestible 
nutrients  will  a  1500-pound  horse  at  light  work 
require  ? 

4.  How  many  pounds  of  oats  would  be  required 
for  37  pounds  of  digestible  protein  ? 

5.  How  many  pounds  of  skim  milk  will  be 
required  to  furnish  .3  pound  of  fats  ? 

Written  Problems 

205.  In  a  feeding  experiment  with  a  large  num- 
ber of  work  horses  at  a  military  post  (Fort  Riley) 
the  following  were  some  of  the  rations  made  use  of 
in  the  tests  calculated  per  1000  pounds  live  weight 
at  light  work : 

Ration  No.  1.  Oats,  10.51  pounds ;  prairie  hay,  12.25 
pounds. 

Ration  No.  2.  Corn,  5.16  pounds ;  bran,  2.58  pounds ; 
linseed  meal,  .86  pound  ;  and  prairie  hay,  12.05  pounds. 

Ration  No.  3.  Oats,  1.70  pounds ;  corn,  6.8  pounds ; 
alfalfa  hay,  8.5  pounds. 

Ration  No.  4.  Oats,  3.39  pounds ;  corn,  5.09  pounds  ; 
bran,  3.39  pounds ;  timothy  hay,  10.17  pounds. 

1.  Find  the  cost  of  each  ration  and  compare  the 
costs,  using  local  prices. 


PRACTICAL  APPLICATIONS  201 

2.  Ration  No.  5  —  oats,  3.36  pounds;  corn, 
6.72  pounds;  prairie  hay,  11.75  pounds  —  was  also 
used  in  the  experiment  mentioned  above.  In  what 
respect  does  this  ration  fail  to  meet  the  needs  of  a 
horse  doing  light  work?  Compare  with  ration 
No.  3  as  to  cost. 

3.  Wherein  will  an  entire  corn  meal  ration  of 
37.2  pounds  fail  to  meet  the  needs  of  a  fattening 
pig  during  the  first  feeding  period  ? 

4.  How  will  the  ration,  corn  meal,  35.7  pounds, 
and  alfalfa  hay,  6.1  pounds,  compare  with  the  feed- 
ing standard  under  the  conditions  of  Problem  3  ? 
Compare  the  cost  of  the  ration  with  the  ration  in 
Problem  3. 

5.  In  a  station  hog-feeding  experiment  the  fol- 
lowing ration  was  found  to  be  one  of  the  most 
satisfactory  for  economical  purposes  for  pork  pro- 
duction :  corn  meal,  23.87  pounds ;  shorts,  8.53 
pounds ;  meat  meal,  1.71  pounds.  The  meat  meal 
used  contained  46  %  protein  and  10  %  fat.  Com- 
pare this  ration  with  the  standard  requirements  for 
fattening  swine  during  the  first  period.  Also,  with 
corn  meal  at  95^  per  hundred,  shorts  at  $1.20  per 
hundred,  and  meat  meal  at  $2.05  per  hundred, 
determine  the  cost  of  the  ration. 

6.  A  farmer  makes  use  of  a  ration  consisting  of 
shelled  corn,  1.23  pounds;  clover  hay,  .78  pound; 
corn  silage,  1.20  pounds,  for  a  lamb.     If  this  is  the 


202  RATIO  AND  PROPORTION 

amount  of  feed  given  daily  to  a  lamb  weighing  75 
pounds,  find  how  nearly  this  meets  his  require- 
ments during  the  first  fattening  period.  Solve  on 
the  supposition  that  the  amount  of  nutrient  re- 
quirements varies  as  the  weight  of  the  animal. 

7.  How  nearly  will  the  following  ration  meet 
the  needs  of  a  1000-pound  two-year-old  steer  dur- 
ing the  second  part  of  the  fattening  period  :  shelled 
corn,  18.47  pounds;  clover  hay,  2.72  pounds;  lin- 
seed meal,  9.42  pounds  ? 

8.  Is  the  following  ration  any  nearer  the  re- 
quirement :  shelled  corn,  22.14  pounds ;  prairie  hay, 
6.8  pounds ;  linseed  meal,  2.46  pounds  ? 

9.  According  to  one  authority  500  pounds  of 
live  weight  of  hens  in  full  laying  require  for 
best  results  the  following  daily  ration :  ash,  1.5 
pounds ;  protein,  5.0  pounds ;  carbohydrates,  18.75 
pounds;  fats,  1.75  pounds.  Find  in  terms  of 
per  cent  the  correct  amount  of  each  food  con- 
stituent for  a  laying  hen. 

(3)    NUTRITIVE   RATIO 

206.  It  has  been  found  that  the  fats  in  a  ration 
contain  about  2^  times  as  much  energy  as  an  equal 
weight  of  carbohydrates  or  protein.  Hence,  in  a 
comparison  of  values  of  these  nutritive  elements, 
the  number  expressing  the  amount  of  fats  must  be 
multiplied  by  2J. 


PRACTICAL  APPLICATIONS  203 

A  narrow  ration  is  one  in  which  the  amount  of 
protein  is  relatively  greater  than  that  of  the  stand- 
ard ration.  A  wide  ration  is  one  in  which  the 
amount  of  protein  is  relatively  less  than  that  of 
the  standard  ration. 

The  nutritive  ratio  of  a  ration  is  the  ratio  of  the 
weight  of  the  protein  to  the  sum  of  the  weights  of 
the  carbohydrates  plus  2^  times  the  fats.  In 
mathematical  formula  we  have, 


Nutritive  ratio  = 


Formula 

Protein 


Carbohydrates  -i-  (2 J  x  fats) 

1.  Find  the  nutritive  ratio  of  the  following 
ration  for  fattening  pigs :  4.5  pounds  of  protein, 
25  pounds  of  carbohydrates,  and  .7  pound  of  fats. 


Solution  by  Formula 

4.5  ^    1 

25 +  (2^  X  .7)     5.91 


Nutritive  ratio  =  — - — -^ =  -— — -  =  1 : 5.91.   Ans. 


Written  Exercise 

207.    Find  the  nutritive  ratios  of  the  following 
rations : 

1.  For  a  horse  at  light  work :  1.5  lb.  protein, 
9.5  lb.  carbohydrates,  and  .4  lb.  fats. 

2.  For  a  dairy  cow :  2.5  lb.  protein,  13  lb.  carbo- 
hydrates, and  .5  lb.  fats. 


204  RATIO  AND  PROPORTION 

3.  For  growing  cattle :  2.5  lb.  protein,  13.2  lb. 
carbohydrates,  and  .7  lb.  fats. 

4.  For  a  horse  at  heavy  work :  2.5  lb.  protein, 
13.3  lb.  carbohydrates,  and  .8  lb,  fats. 

Written  Problems 

208.  1.  Find  the  nutritive  ratio  of  the  ration 
consisting  of  corn  fodder,  12  pounds;  clover  hay, 
6  pounds;  corn  meal,  5  pounds;  wheat  bran,  2 
pounds. 

2.  Find  the  nutritive  ratio  of  a  ration  consisting 
of  corn  silage,  32  pounds ;  clover  hay,  8  pounds ; 
corn  meal,  4^  pounds ;  cottonseed  meal,  1^  pounds. 

3.  Find  the  nutritive  ratio  of  the  feeding  stand- 
ards in  the  table  on  page  199. 

4-8.  Find  the  nutritive  ratio  of  the  rations 
Nos.  1  to  5,  page  200. 

9.  Compare  the  nutritive  ratio  of  the  following 
rations  for  a  milch  cow  giving  22  lb.  of  milk  daily 
with  that  of  the  feeding  standard.  Find  which  is 
narrow  and  which  is  wide.  Note  which  one  more 
nearly  meets  the  requirements  of  the  balanced 
ration : 

Ration  I.  Clover  hay  18  pounds,  wheat  bran  5  pounds, 
corn  meal  6  pounds,  linseed  rieal  1  pound. 

Ration  II.  Alfalfa  hay  15  pounds,  wheat  bran  5  pounds, 
corn  meal  6  pounds. 

10.  In  feeding  a  lot  of  10  pigs,  whose  average 
weight  is  147  pounds,  a  daily  ration  of  5.52  pounds 


PRACTICAL  APPLICATIONS 


205 


per  head  consisting  of  8  parts  corn  meal  and  one 
part  linseed  meal  is  used.  Find  the  nutritive  ratio. 
Is  this  a  wide  or  narrow  ration  for  a  fattening  pig 
during  the  first  fattening  period  ? 

(4)    BALANCED    RATIONS 

209.  The  practical  problem  before  the  farmer 
and  stock  feeder  of  compounding  a  suitable  ration, 
in  view  of  the  fact  that  feeds  are  not  always  avail- 
able, that  market  prices  vary,  and  that  other  con- 
ditions must  be  figured  in,  must  usually  be  solved 
by  trial.  The  exact  calculation  of  balanced  rations 
has  been  worked  out  mathematically  by  various 
writers.  However,  since  a  somewhat  unbalanced 
ration  is  at  times  the  better  one,  all  things  con- 
sidered, and  feeding  standards  are  but  guides,  the 
method  of  approximation  by  trial  will  be  illustrated 
here. 

First  Trial  Ration  for  a  Dairy  Cow  Yielding  22  Pounds 
OF  Milk  Daily 


Feeding  Stuffs 

Protein 

Cabhoiivdrates 

Fat 

NUTRITIVE 

Katio 

Red  clover  hay,  8  lb.   . 
Corn  stover,  12  lb.  .     . 
Corn  meal,  5  lb.      .     . 
Wheat  bran,  6  lb.    .     . 

.590 
.238 
.313 
.721 

3.052 
3.979 
3.263 
2.474 

.145 
.068 

.175 

.172 

1:5.7 
1:17.4 
1:11.7 
1:4.0 

First  trial  ration     .     . 
Standard  ration .     .     . 

1.862 
2.500 

12.768 
13  000 

.560 
.500 

1:6  5 
1 : 5.7 

206 


RATIO  AND  PROPORTION 


This  trial  ration,  on  comparing  with  the  stand- 
ard, is  seen  to  be  considerably  deficient  in  protein. 
To  make  it  approximate  the  balanced  form,  2 
pounds  of  cottonseed  meal  are  added. 

Second  Trial  Ration  for  a  Dairy  Cow  Giving  22 
Pounds  of  Milk  Daily 


Feeding  Stdffs 

Protein 

Carbohydrates 

Fat 

Nutritive 
Ratio 

First  trial  ration      .     . 
Cottonseed  meal,  2  lb. 

1.862 
.740 

12.768 
.330 

.560 
.252 

1 : 7.5 
1:1.2 

Second  trial  ration  .     . 
Standard  ration  .     .     . 

2.602 
2.500 

13.098 
13.000 

.812 
.500 

1:5.7 

1 : 5.7 

All  the  nutrients  in  the  second  trial  ration  are 
in  slight  excess,  and  the  nutritive  ratio  is  close  to 
the  standard.  Hence,  this  ought  to  give  satisfac- 
tory results. 

Written  Exercise 

210.  With  the  following  scale  of  prices,  barley, 
65^;  corn,  55^;  oats,  38J^ ;  bran,  $20  per  ton; 
alfalfa  hay,  $10;  timothy  hay,  $12.50;  prairie 
hay,  $12.50;  alfalfa  meal,  $14  per  ton;  linseed 
meal,  $  35  per  ton  ;  and  silage,  $  6  per  ton,  make 
up  a  balanced  ration  for : 

1.  A  horse  doing  light  work. 

2.  A  horse  doing  heavy  work. 

3.  A  cow  giving  IQ^  pounds  of  milk  daily. 

4.  A  cow  giving  22  pounds  of  milk  daily. 


PRACTICAL  APPLICATIONS 


207 


5.  Fattening  cattle  during  the  first  period. 

6.  Fattening  swine  during  the  first  period. 

7.  Any  other  animal  raised  in  your  locality  us- 
ing local  feeds  and  prices. 


(5)    SILOS 

211.  The  silo  makes  it  possible  to  preserve  fodder 
in  its  green,  succulent  state  for  feeding  farm  animals, 
better  than  is  possible  by  any  other  system  of  pres- 
ervation now  known.  Most  of  the  present-day 
silos  are  built  above  the 
ground  from  such  ma- 
terial as  wood,  cement, 
steel,  brick,  hollow  tile, 
etc.  Some  silos  are  built 
square  or  polygonal,  but 
the  round  silo  gives  the 
best  satisfaction. 

In  the  construction  of 
a  silo  it  is  very  impor- 
tant to  have  the  horizon- 
tal dimensions  such  that 
not  less  than  1|  inches  of 
the  top  layer  of  the  silage 
will  be  fed  out  daily  in 
order  to  prevent  it  from 
spoiling.  The  diameter  of  the  silo  must,  therefore, 
be  planned  according  to  the  size  of  the  herd. 


208 


RATIO  AND  PROPORTION 


The  following  table  shows  the  computed  average 
weight  of  well-matured  corn  silage  for  silos  of  dif- 
ferent depths,  two  days  after  filling.  (FrouiKing's 
Physics  of  A  griculture . ) 


Depth 

Wkight  per 
Cubic  Foot 

Depth 

Wbiuht  per 
Cubic  Foot 

Depth 

Weight  pek 
Cubic  Foot 

10 

26.1 

19 

32.6 

28 

38.4 

11 

26.8 

20 

33.3 

29 

39.0 

12 

27.6 

21 

33.9 

30 

39.6 

13 

28.3 

22 

34.6 

31 

40.1 

14 

29.1 

23 

35.3 

32 

40.7 

15 

29.8 

24 

35.9 

33 

41.2 

IG 

30.5 

25 

36.5 

34 

41.8 

17 

31.2 

26 

37.2 

35 

42.3 

18 

31.9 

27 

37.8 

36 

42.8 

Written  Exercise 

212.    1.    Find  the  perimeters  and  areas   of   the 
following  figures : 

{a)  A  rectangle  12  by  20  feet. 
(h)  A  square  16  feet  on  each  side, 
(c)  A  circle  20  feet  in  diameter. 

2.    Compare  the  amount  of  wall  surface  in  the 
following  silos : 

{a)  A  silo  with  a  rectangular  base  12  by  20, 

and  30  feet  high. 
{h)  A  silo  16  by  16,  by  30  feet  high, 
(c)  A  silo  with  a  circular  base   20  feet  in 
diameter  and  30  feet  high. 


PRACTICAL  APPLICATIONS  209 

3.  If  a  cubic  foot  of  silage  weighs  40  pounds, 
how  many  tons  will  each  silo  in  problem  2  hold? 

4.  How  many  2  by  6  staves  would  be  required 
to  build  each  of  the  silos  in  problem  2 ;  and  what 
would  be  the  cost  of  the  staves  for  each  at  $  30  per 
thousand  ? 

Written  Problems 

213.  1.  What  is  the  capacity  in  tons  of  a  silo  20 
feet  in  diameter  and  32  feet  high? 

2.  The  amount  of  silage  that  should  be  fed  from 
such  a  silo  to  keep  the  surface  of  the  silage  from 
spoiling  is  about  2100  pounds.  How  many  inches 
in  depth  will  be  fed?  If  a  cow  eats  45  pounds 
daily,  how  many  cows  should  be  kept  to  use  the 
silage  fast  enough  to  keep  it  from  spoiling  ? 

3.  An  eighteen-acre  field  yields  11.37  tons  of 
silage  per  acre.  What  must  be  the  height  of  a 
20-foot  silo  to  hold  it  if  one  cubic  foot  of  silage 
weighs  40.7  pounds?  (Give  the  result  to  the 
nearest  whole  number.) 

4.  A  farmer  estimates  that  he  will  need  196  tons 
of  silage  for  the  winter.  He  has  purchased  staves 
intended  for  a  silo  36  feet  high.  What  will  be  the 
diameter  if  one  cubic  foot  of  silage  weighs  42.8 
pounds?     (Give  result  to  nearest  whole  number.) 

5.  A  cow  should  be  fed  about  40  pounds  of 
silage  per  day.     What  should  be  the  diameter  of  a 


210  RATIO  AND  PROPORTION 

24-foot  silo  in  order  that  1^  inches  in  depth  may 
be  fed  out  daily  to  a  herd  of  1 2  cows  ? 

6.  Fattening  beef  cattle  should  be  fed  about  25 
pounds  a  day.  What  should  be  the  diameter  of  a 
30-foot  silo  if  2  inches  in  depth  are  fed  daily  to  a 
herd  of  60? 

7.  A  silo  is  20  feet  in  diameter  and  36  feet 
high.  What  is  the  least  number  of  cows  that 
must  be  kept  to  prevent  the  silage  from  spoiling 
if  each  cow  is  fed  40  pounds  daily  ? 

8.  What  should  be  the  size  of  a  silo  for  a  herd 
of  25  cows  that  are  to  be  fed  40  pounds  a  day  for 
180  days  at  the  rate  of  2  inches  of  depth  a  day? 
(Give  results  in  nearest  whole  numbers.) 

9.  What  should  be  the  size  of  a  silo  for  a  herd 
of  60  fattening  cattle  fed  30  pounds  a  day  for  216 
days  at  the  rate  of  2  inches  of  depth  per  day? 
(Give  results  in  nearest  whole  numbers.) 

10.  What  must  be  the  diameter  of  a  silo  to  hold 
twice  as  much  as  a  silo  30  feet  high  and  20  feet  in 
diameter  if  their  heights  are  the  same? 

11.  Some  authorities  estimate  that  5  square  feet 
of  horizontal  feeding  surface  should  be  allowed  for 
each  cow.  What  should  be  the  diameter  of  a  silo 
for  a  herd  of  36  cows? 

12.  Allowing  5  square  feet  per  cow  as  in  prob- 
lem 11,  what  should  be  the  diameter  of  a  silo  for 
a  herd  of  45  cows? 


PROPORTION  211 

13.  From  29,800  pounds  of  green  fodder  turned 
into  silage  fed  with  hay  and  grain,  7496  pounds 
of  milk,  containing  340.4  pounds  of  fat,  were  pro- 
duced ;  and  from  the  same  number  of  pounds  of 
green  fodder,  field-cured,  fed  with  the  same  amount 
of  hay  and  grain,  7119  pounds  of  milk  and  318.2 
pounds  of  fat  were  produced.  What  was  the  per 
cent  of  increase  in  the  amount  of  milk  ?  In  the 
amount  of  butter  fat? 

14.  In  an  experiment  with  silage  for  fattening 
cattle  at  the  Kansas  station,  it  was  found  that  156 
pounds  of  alfalfa  hay  was .  equivalent  in  feeding 
value  to  461  pounds  of  silage.  If  alfalfa  hay  is 
worth  S  12.50  per  ton,  what  is  the  value  of  silage 
per  ton  ? 

15.  If  a  silo  is  18  feet  in  diameter,  inside  measure, 
and  32  feet  high,  how  many  cubic  yards  of  concrete 
will  it  take  to  build  it  if  the  wall  and  floor  are  each 
6  inches  thick,  and  the  foundation  is  8  inches  thick 
and  5  feet  deep? 

16.  If  a  1 :  IJ :  3  mixture  is  used,  how  many 
sacks  of  cement,  cubic  yards  of  sand,  and  cubic 
yards  of  gravel  will  be  needed  ? 

PROPORTION 

Study  Exercise 

214.  Proportion  is  a  statement  of  the  equality 
between  two  ratios.     It  is  written  in  two  ways,  as 


212  RATIO  AND  PROPORTION 

indicated  in  the  following  example  :  3  :  5  =  18  :  30 
or  3  :  5  : :  18  :  30.  In  either  form  it  is  read  3  is  to  5 
as  18  is  to  30  and  means  the  same  as  |^  =  ^. 
Any  proportion  may  be  written  in  the  fractional 
form. 

The  extremes  of  a  proportion  are  the  first  and 
last  terms ;  and  the  means  are  the  second  and  third 
terms.  The  antecedents  are  the  first  and  third  terms, 
and  the  consequents  are  the  second  and  fourth.  In 
most  of  the  simple  problems  of  proportion  the 
following  important  fact  is  used :  viz.,  The 
product  of  the  means  is  equal  to  the  product  of 
the  extremes.  Thus  :  in  4  :  3  =  12  :  9,  the  product 
of  the  extremes  is  36,  as  is  also  the  product  of  the 
means. 

From  the  above  principle  the  following  two  prac- 
tical rules  concerning  the  terms  of  a  proportion  are 
easily  derived : 

1.  Either  extreme  equals  the  product  of  the 
means  divided  by  the  other  extreme. 

2.  Either  mean  equals  the  product  of  the  ex- 
tremes divided  by  the  other  mean. 

1.  Find  the  value  of  x  in  the  proportion  16  :  25 
=  12:a;. 

Process 
16  :  25  =  12  :  oj  Explanation :    Product    of 

16  a;  =  25  x  12  means  equals  the  product  of 

16  a;  =  300  extremes. 

x=^^  =  18f .     Ans. 


PROPORTION  213 

Written  Exercise 

215.   Find  the  values  of  x  in  the  following  pro- 
portions : 


1. 

a;:  39::  15:  13. 

6. 

179.2  :cc::  25.6:  5.1 

2. 

95:  a;::  19:  5. 

7, 

a;:  4.15::  65:  7.2. 

3. 

108:  93:: a;:  31. 

8. 

8f:14f::25i:x. 

4. 

680:36::70:x. 

9. 

7|:4f::x:9. 

5. 

22:x::34:55. 

10. 

x:  13::  14:  117. 

Written  Problems 

216.  1.  If  8  tons  of  coal  cost  $46,  what  will  25 
tons  cost  at  the  same  rate  ? 

This  problem  can  be  put  into  the  form  of  a  pro- 
portion, since  the  same  relation  holds  between  the 
amounts  of  coal  as  between  the  cost  prices.  Hence, 
we  have  8  :  25  : :  $  46  :  $  x. 

2.  An  express  train  runs  50  miles  in  70  minutes. 
At  the  same  rate,  how  many  miles  will  it  run  in  40 
minutes? 

3.  Assuming  the  ratio  of  the  circumference  of  a 
circle  to  the  diameter  as  -^y^-,  find  the  circumference 
of  a  fly  wheel  8  feet  in  diameter. 

4.  If  a  farmer  sells  5  tons  of  hay  for  $  45,  how 
much  will  he  receive  for  20  tons  at  the  same 
rate? 

5.  If  6  men  can  do  a  piece  of  work  in  15  days, 
how  long  will  it  take  10  men  to  do  the  same  work? 


214  RATIO  AND  PROPORTION 

6.  If  a  post  24  feet  high  casts  a  shadow  32  feet 
long,  at  the  same  time  how  long  is  the  shadow  of 
a  tree  which  is  80  feet  high  ? 

7.  The  height  of  a  tall  object  may  be  found  by 
means  of  proportion.  The  accompanying  figure 
shows  how  to  measure  the  height  of  a  tree.     The 

g  man  holds  a  right  triangle  in 
which  AB  equals  BC.  Keeping 
AB  level,  he  moves  until  the 
top  of  the  tree  just  comes  in 
line  with  A  C.  Since  the  propor- 
tion AB.BC.-.AD.DE  holds 

D 

where  AB  equals  BC,  it  follows 
that  AD  equals  DE.  Hence,  it  follows  that  the 
entire  height  of  the  tree  is  readily  found  by  a  hori- 
zontal ground  measurement. 

8.  A  farmer  in  planting  potatoes  used  two 
different  sizes  for  seed.  The  small  seed  yielded 
141  bushels  per  acre,  and  the  large  28  %  more. 
Find  the  yield  in  bushels  per  acre  of  the  large  seed. 

9.  If  in  10  pounds  of  a  certain  fertilizer  there 
are  .47  pound  of  nitrogen,  .988  pound  of  phos- 
phorus, and  .478  pound  of  potash,  how  many  pounds 
of  each  of  these  are  there  in  one  ton  of  fertilizer  ? 

10.  At  the  Kansas  Experiment  Station  in  1912, 
the  total  yield  of  alfalfa  for  the  season  in  pounds 
per  acre  was  5370  on  a  fertilized  plot  and  4390 
on  an  unfertilized  plot.     The  value  of  the  yield  per 


PROPORTION  215 

acre  of  the  unfertilized  plot  was  $21.95  and  the 
cost  of  fertilizing  was  $2.09.  Determine  the  net 
increase  in  financial  returns  per  acre  due  to  fer- 
tilizing. 

11.  If  in  corn  there  is  10.6%  water,  1.5%  ash, 
10.3  %  protein,  72.6  %  carbohydrates,  and  5  %  fats, 
how  much  of  each  of  these  is  there  in  3000  pounds 
of  corn  ? 

12.  A  fertilizer  has  4.54  %  of  nitrogen,  7.82  %  of 
phosphoric  acid,  7.94  %  of  potash.  Find  the  price 
of  a  ton  of  the  fertilizer  if  nitrogen  is  worth  17i^ 
per  pound,  pho'sphoric  acid  4.5 i^,  and  potash  h^. 

13.  If  8  bushels  of  wheat  will  seed  5  acres  of 
land,  how  many  bushels  will  be  required  to  seed  a 
field  60  rods  wide  and  95  rods  long  ? 

14.  A  garrison  of  480  men  has  provisions  to  last 
during  a  certain  period  at  the  rate  of  2  pounds, 
4  ounces  per  day  for  each  man.  If  the  allowance 
is  reduced  to  1  pound,  4  ounces  per  day,  how  many 
men  could  be  added  to  the  garrison  ? 

15.  If  4  pounds  of  cotton-seed  meal  are  equal  to 
7  pounds  of  corn  for  cattle  feeding,  what  is  the 
value  of  a  ton  of  cotton-seed  meal  for  cattle  feeding 
when  corn  is  worth  45^  a  bushel? 

16.  Measure  the  height  of  a  post  and  the  length 
of  its  shadow;  also,  at  the  same  time,  measure 
the  length  of  the  shadow  of  some  tall  object,  and 
calculate  its  height. 


APPLICATIONS   OF   PROPORTION 
LEVERS 

217.  A  lever  is  a  rigid  rod  which  can  be  moved 
freely  about  a  fixed  point.  The  principle  of  the 
lever  is  an  important  one  and  enters  into  such 
common  implements  as  the  hammer,  crowbar,  etc. 
In  the  theory  of  levers  three  elements  must  be 
considered : 

(1)  The  power  applied. 

(2)  The  weight  moved. 

(3)  The  fulcrum,  or  fixed  point  on  which  the 
lever  turns. 

In  the  accompanying  figure  F  stands  for  the  ful- 
crum, W  for  the  weight,  P  for  the  power,  d"  for  the 

di d;^ 

W  A  F  P 

distance  from  the  fulcrum  to  the  point  of  applica- 
tion of  the  force,  and  d'  for  the  distance  from  the 
fulcrum  to  the  point  where  the  weight  is  attached. 
The  following  proportion  holds  in  all  cases : 
W:P::d":d'. 

Oral  Exercise 

218.  1-  In  the  foregoing  figure,  if  the  fulcrum 
is  moved  toward  the  weight,  what  will  be  the  effect 
upon  the  force  required  to  lift  the  weight? 

216 


APPLICATIONS  OF  PROPORTION  217 

2.  Answer  the  corresponding  question  in  case 
the  fulcrum  is  moved  toward  the  point  of  applica- 
tion of  the  power. 

3.  li  d'  and  d"  are  equal  to  4  and  1  respectively, 
how  many  pounds  must  be  exerted  to  lift  a  weight 
of  80  pounds  ?     Of  120  pounds  ? 

4.  Under  the  same  conditions  as  in  exercise  3, 
how  heavy  a  weight  can  be  lifted  by  applying  a 
force  of  25  pounds  ?     Of  40  ?     Of  7i  ? 

5.  Locate  the  fulcrum,  weight,  and  power  in  a 
pair  of  scissors ;  in  nutcrackers. 

Written  Problems 

219.  1.  A  man  weighing  150  pounds,  wishing  to 
raise  a  stone,  puts  his  weight  on  the  end  of  a 
straight  crowbar,  4^  feet  long,  which  rests  on  a 
block  5  inches  from  the  stone.  What  force  does 
he  exert  on  the  stone  ? 

2.  In  a  pair  of  nutcrackers  the  nut  is  placed  at 
a  distance  of  IJ  inches  from  the  hinge.  With  a 
pressure  of  60  pounds  exerted  at  the  distance  of 
8  inches  from  the  hinge,  how  much  resistance  can 
be  overcome  ? 

3.  Two  children,  playing  seesaw  at  opposite  ends 
of  a  plank  14  feet  long,  weigh  48  pounds  and  70 
pounds  respectively.  Find  the  distance  of  each 
child  from  the  fulcrum. 


218  RATIO  AND  PROPORTION 

4.  With   steelyards  as  in  the  adjoining  figure, 

what  must  be  the  weight,  P,  to  balance  a  weight, 

-        j 

J  j 

p  w 

TF^  of  20  pounds  if  it  is  2 J  inches  from  the  fulcrum 

to  the  application  of   W  and  12  inches  from  the 

application  P  ? 

5.  In  cutting  a  piece  of  tin  with  a  pair  of  shears, 
the  point  of  contact  with  the  tin  is  |-  inch  from  the 
fulcrum,  and  the  pressure  is  exerted  at  a  distance  of 
7  inches  from  the  fulcrum.  Find  the  force  exerted 
by  the  hand  if  the  resistance  of  the  tin  is  480  pounds. 

6.  In  pulling  a  nail  from  a  board  with  a  hammer, 
the  distance  from  the  fulcrum  to  the  nail  is  IJ 
inches  and  from  the  fulcrum  to  the  hand  is  lOJ 
inches.  Find  the  resistance  of  the  nail  for  a  pull 
of  80  pounds  upon  the  hammer  handle. 

7.  A  safety  valve  is  set  to  pop  at  160  pounds 
per  square  inch.  The  short  arm  lever  is  3  inches, 
the  long  arm  15  inches.  The  diameter  of  the 
valve  is  2  inches.  What  weight  must  be  attached 
to  the  lever  ? 

15 


6 


w 


8.    If  a  weight  of  10  pounds  is  fastened  to  the 
long  arm  of  the  lever,  at  what  pressure  will  it  pop  ? 


GENERAL   REVIEW 

MISCELLANEOUS    PROBLEMS 

220.  1.  Zintheo  figures  that  the  depreciation  in 
value  of  a  corn  harvester  is  $22.50  per  year.  If 
the  twine  and  labor  cost  75  ^  per  acre,  what  is  the 
cost  of  harvesting  10  acres,  not  counting  the  shock- 
ing and  hauling  to  the  silo  ?  If  the  cost  of  har- 
vesting by  hand  is  $1.50  per  acre,  which  is  the 
cheaper  plan  of  harvesting  and  how  much  ?  If 
the  shocking  costs  45^  and  hauling  to  the  silo 
Sl.lO  per  acre,  what  is  the  total  cost  per  acre 
when  the  harvester  is  used  ? 

2.  Find  the  cost  of  material  needed  to  make  a 
green  sand  mold  as  follows :  Green  sand  or  mold- 
ing sand,  25  pounds  at  |^^  per  pound,  1  pound  of 
sea  coal  at  1^^  per  pound,  2  pounds  of  parting 
sand  at  |-j^  per  pound,  4  patterns  at  5|-)^  each,  and 
J  pound  of  graphite  at  15  )^  per  pound. 

3.  A  field  is  ^  mile  long  and  J  mile  wide.  If 
a  gang  plow  cuts  28  inches,  how  many  acres  does 
a  man  plow  in  9  rounds  ? 

4.  Sprayed  grapes  yielded  3  pounds  4:-^q  ounces 
more  per  row  than  un sprayed  grapes.  What  was 
the  increased  yield  on  17  rows? 

219 


220  GENERAL  REVIEW 

5.  How  many  plants  can  be  set  on  a  plot  15 
feet  square  so  that  no  two  will  be  nearer  than  ^ 
foot  apart  ?     Illustrate  with  drawing. 

6.  What  will  it  cost  to  build  a  concrete  walk 
3  feet  wide  around  the  outside  of  an  80-foot  square 
court  at  13^  per  square  foot? 

7.  A  fence  around  a  square  field  costs  $35.20 
at  16)^  per  rod.  What  would  have  been  the  cost 
if  the  field  had  been  in  the  form  of  a  rectangle 
with  a  width  of  45  rods? 

8.  How  long  must  a  tape  line  be  to  wind  a 
spiral  around  a  cylinder  that  is  50  feet  long  and 
8  feet  in  circumference,  if  it  passes  once  around  in 
every  6  feet  of  the  cylinder's  length  ? 

9.  A  field  is  40  by  20  rods.  What  will  it  cost 
to  put  a  wire  fence  around  it  at  22  ^  per  rod  for 
the  wire  and  17  (^  for  each  post,  if  the  posts  are 
one  rod  apart  ? 

10.  A  field  is  80  rods  long  and  35  rods  wide. 
What  is  the  width  of  a  similar  field  whose  length 
is  48  rods  ? 

11.  A  border  is  to  be  placed  about  a  square  with 
an  area  that  is  one  half  of  the  square.  If  the  side 
of  the  square  is  8  inches,  what  are  the  outside 
dimensions  of  the  border? 

12.  Show  that  the  area  of  a  square  circumscribed 
about  a  circle  8  inches  in  diameter  is  twice  the  size 
of  a  square  inscribed  in  the  same  circle. 


MISCELLANEOUS  PROBLEMS  221 

13.  What  is  the  depth  of  a  cubical  vat  that  holds 
ten  gallons  of  water? 

14.  Draw  to  scale  of  J  inch  to  the  rod,  a  diagram 
of  a  rectangular  field  24  by  30  rods.  What  would 
be  the  value  of  the  land  at  $75  per  acre? 

15.  A  ten-acre  field  in  the  form  of  a  square  was 
laid  out  into  lots.  A  strip  30  feet  wide  was  taken 
from  each  of  the  sides.  The  field  was  now  divided 
into  four  lots  by  alleys  running  full  length  through 
the  center.  Both  alleys  were  60  feet  wide.  What 
were  the  dimensions  of  the  lots?  Draw  to  scale, 
using  ^  inch  to  the  rod. 

16.  One  of  the  bases  of  a  trapezoid  is  10  feet, 
the  altitude  is  4  feet,  and  the  area  is  32  square 
feet.  What  is  the  length  of  a  line  between  the 
bases  and  parallel  to  them  that  is  1  foot  distant 
from  the  10-foot  base  ? 

17.  A  room  is  24  by  18  by  10  feet.  What  will 
it  cost  to  plaster  the  room  at  20  ^  per  square  yard, 
making  deductions  for  two  doors,  6  by  3 J  feet; 
three  windows,  6  by  3  feet;  and  a  9-inch  base- 
board ? 

18.  Find  the  weight  of  wheat  that  will  fill  a  bin 
8  by  6  by  5  feet. 

19.  What  is  the  cost  of  3260  pounds  of  oats  at 
40^  per  bushel  and  4680  pounds  of  wheat  at  95^ 
per  bushel  ? 


222  GENERAL  REVIEW 

20.  Ten  loads  of  corn  weigh  3200,  3150,  3280, 
2860,  2950,  2870,  2900,  3140,  3300,  3080  pounds, 
respectively.  What  will  the  corn  bring  at  58  ^  per 
bushel  ? 

21.  If  a  railway  right-of-way  is  66  feet  wide, 
how  many  miles  in  length  must  it  be  to  contain  an 
acre? 

22.  If  you  multiply  the  diameter  of  a  circle  by 
.7071,  the  result  is  the  side  of  an  inscribed  square. 
Why  is  this  ? 

23.  Show  that  it  will  take  350  posts  8  feet  apart 
for  a  fence  inclosing  a  field  that  is  600  by  800 
feet. 

24.  A  cistern  is  6  feet  in  diameter.  How  much 
will  a  one-inch  rain  upon  a  roof  that  is  60  by  40 
feet  raise  the  level  of  the  water? 

25.  An  ordinary  lead  pencil  is  6  inches  long  and 
J  inch  in  diameter.  If  the  lead  in  the  pencil  is  ^g 
inch  in  diameter,  what  is  the  volume  of  the  entire 
pencil  ?     Of  the  lead  ?     Of  the  wood  ? 

26.  A  box  is  to  be  made  8  feet  3  inches  by  4 
feet  9  inches  by  3  feet  11  inches,  inside  measure- 
ments. How  much  1-inch  lumber  will  it  take  to 
make  the  box  without  a  lid  ? 

27.  An  excavation  for  a  cellar  is  60  by  30  by  8 
feet.  How  many  cubic  feet  of  concrete  are  in  the 
walls  if  they  are  18  inches  thick  ? 


MISCELLANEOUS  PROBLEMS  223 

28.  A  contractor  agreed  to  furnish  the  paint  and 
give  two  coats  to  five  ceilings  that  were  30  by  27 
feet,  for  $  75.  What  was  the  cost  per  square  yard 
to  the  owner? 

29.  I  measure  directly  east  from  a  point  ^  to  a 
point  B,  then  north  144  feet  to  a  point  C.  From 
point  C  I  measure  directly  east  again  to  a  point  D, 
a  distance  of  160  feet.     What  is  the  distance  BD1 

30.  A  cylindrical  water  tank  is  18  feet  in  diam- 
eter and  30  feet  high.  If  it  is  J  full,  what  will  be 
the  weight  of  the  water  in  the  tank  ? 

31.  On  a  strip  of  ground  100  by  80  feet  a  boy 
raises  122  bushels  of  potatoes.  At  the  same  rate, 
what  would  be  the  yield  per  acre  ? 

32.  If  corn  is  planted  so  that  the  hills  are  3  feet 
8  inches  apart,  what  will  be  the  number  of  hills  to 
the  acre  ? 

33.  Show  that,  if  you  multiply  the  side  of  a 
square  inscribed  in  a  circle  by  1.4142,  the  result  is 
the  side  of  a  circumscribed  square. 

34.  Dwarf  pear  trees  are  usually  15  feet  apart 
each  way.     How  many  trees  per  acre  ? 

35.  What  will  14  bushels  3  pecks  4  quarts  of 
charcoal  cost  at  62  ^  per  bushel  ? 

36.  At  %  690.75  per  mile,  what  is  the  cost  of  a 
road  17  miles  long  ? 

37.  How  many  square  yards  of  plastering  will  be 
required  for  the  ceiling  and  walls  of  a  room  10  by  15 


224  GENERAL  REVIEW 

by  9  feet  ?     The  room  has  one  door  3|-  by  7  feet, 
three  windows  3 J  by  6  feet,  and  an  8-inch  baseboard. 

38.  Find  the  area  of  a  flat  circular  ring  whose 
outside  diameter  is  12  inches  and  inside  diameter 
6  inches. 

39.  A  body  floating  in  water  displaces  its  own 
weight.  A  battleship  weighs  31,400  tons.  How 
many  gallons  of  water  does  it  displace  ?  How 
many  cubic  feet  ? 

40.  How  many  cubic  feet  of  concrete  are  there 
in  a  battered  retaining  wall  15  feet  high,  2  feet 
thick  at  the  top,  and  5  feet  thick  at  the  bottom,  and 
50  feet  long  ?  How  many  sacks  of  cement  will  be 
required  for  the  wall  if  a  1 :  3  :  6  mixture  is  used  ? 

41.  Find  the  diameter  of  the  down  spout  of  a 
roof  60  by  120  feet,  using  1  square  inch  of  pipe 
area  for  every  175  feet  of  roof  area. 

42.  Find  the  diameter  for  a  cast-iron  bearing 
plate  for  a  column  load  of  40,000  pounds  on  a 
concrete  pier,  allowing  200  pounds  per  square  inch 
as  a  safe  strength  of  concrete. 

43.  Find  the  weight  of  a  cast-iron  column  10 
feet  long,  10  inches  in  diameter,  and  1  inch  thick, 
if  cast  iron  weighs  450  pounds  per  cubic  foot. 

44.  To  irrigate  a  20-acre  field  water  is  run  full 
bore  through  a  6-inch  pipe  with  a  velocity  of  one 
foot  per  second.  How  long  will  it  take  to  deliver 
one  inch  of  water  over  the  entire  field  ? 


MISCELLANEOUS  PROBLEMS 


225 


45.  In  a  certain  town  a  cylindrical  water  tank 
48  feet  in  diameter  is  lowered  5  feet,  when  no 
water  is  being  pumped  into  it,  in  5  hours  and  30 
minutes.  How  many  gallons  are  being  removed 
per  hour  ? 

46.  A  cow  is  tied  to  the  corner  post  of  a  rec- 
tangular field  by  a  rope  40  feet  long.  Over  what 
part  of  an  acre  can  she  feed  ? 

47.  How  many  acres  of  corn  will  it  require  to 
produce  the  silage  to  feed  20  cows  36  pounds  each 
day  for  120  days,  if  each  acre  yields  12J  tons  of 
silage?  What  must  be  the  diameter  of  the  silo 
necessary  to  hold  this  silage  if  its  height  is  24  feet, 
and  one  cubic  foot  of  silage  weighs  35  pounds  ? 

48.  Make  a  graphic  chart,  illustrating  the  mois- 
ture content  of  three  adjoining  fields  cropped  to 
alfalfa,  wheat,  and  corn,  respectively,  soil  samples 
in  the  experiment  being  taken  to  a  depth  of  six 
feet.  Use  straight  lines  in  the  drawings  obtained 
from  the  following  data  : 


Month 

AMT.   of   MoiSTtTEE 

IN  Inches 

Month 

Amt.  of  Moisture 
IN  Inches 

Alfalfa 

Wheat 

Corn 

Alfalfa 

Wheat 

(.'orn 

Jan.  ..   . 
Feb.  .     . 
Mar.  .     . 
April 
May  .     . 
June .     . 

17.1 
17.0 
17.4 
13.7 
11.6 
15.2 

22.8 

21.9 
21.8 
17.2 
15.3 
20.3 

23.0 
19.0 
22.5 
19.6 
21.2 
22.9 

July  .     . 

Aug.       . 
Sept.      . 
Oct.  .     . 
Nov. .     . 
Dec.  .     . 

12.2 
12  5 
12.3 
12.1 
13.6 
12.1 

183 
18.7 
18.4 
19.6 
19.8 
17.5 

16.0 
17.0 
16.5 
18.3 
19.2 
16.8 

226 


GENERAL  REVIEW 


49.  Represent  graphically  the  results  of  the  fol- 
lowing experiment  at  the  Illinois  station  to  deter- 
mine the  effects  upon  milk  production  of  a  balanced 
ration.  The  data  give  the  weekly  milk  production 
per  cow  of  lots  I  and  II  of  a  dairy  herd  fed  on  a 
balanced  ration  and  an  unbalanced  ration,  re- 
spectively : 


TlMB 

Pounds  of  Milk 
PEK  Week 

Time 

Pounds  of  Milk 
per  Week 

Lot  I 

Lot  II 

Lot  I 

Lot  II 

Jan.    7  . 
Jan.  14  . 
Jan.  21  . 
Jan.  28  . 
Feb.    4  . 
Feb.  11  . 

257 
243 
245 
251 
252 
247 

216 
202 
192 
184 
174 
169 

Feb.  18  . 
Feb.  25  . 
Mar.    4 . 
Mar.  11 . 
Mar.  18 . 
Mar.  25  . 

250 
251 
244 
2^6 
221 
219 

160 
162 
157 
149 
144 
143 

Judge  from  the  space  between  the  two  graphs 
as  to  the  difference  in  milk  production. 

50.  Water  enters  a  tank  through  two  pipes  hav- 
ing diameters  of  J  inch  and  IJ  inches,  respectively. 
Find  the  size  of  the  waste  pipe  that  will  allow  the 
water  to  run  out  as  fast  as  it  runs  in. 

51.  If  the  fire  under  a  steam  boiler  requires  4 
pounds  of  coal  per  horsepower  per  hour,  find  the 
cost  of  coal  at  $4.25  per  ton  to  run  a  150-horse- 
power  boiler  for  20  days  of  10  hours  each. 

52.  On  a  poor  road  a  farmer  can  haul  ^  ton  at 
a  load,  and  on  a  good  road  IJ  tons.     Allowing 


MISCELLANEOUS  PROBLEMS  227 

three  loads  per  day  on  a  poor  road  and  four  loads 
per  day  on  a  good  road,  what  is  the  loss  at  $  3.75 
per  day  in  marketing  over  the  poor  road  675 
bushels  of  corn  (70  pounds  per  bushel)  ? 

53.  The  trade  route  from  San  Francisco  to  New 
York  is  5240  miles  by  way  of  the  Panama  Canal. 
This  is  62  %  shorter  than  the  route  by  Cape  Horn. 
What  is  the  length  of  the  route  by  Cape  Horn  ? 

54.  Wheat  loses  about  IS  %  by  weight  when 
ground  into  flour.  How  many  bushels  are  required 
to  make  a  barrel  of  flour  (196  pounds)  ? 

55.  If  wheat  is  worth  $1  per  bushel  and  a  barrel 
of  flour  sells  for  $  4.85,  what  is  the  amount  received 
for  milling  and  packing  ? 

56.  How  many  12-ounce  loaves  of  bread  can  be 
made  from  a  barrel  of  flour  if  the  weight  of  the 
bread  is  133-|%  of  the  weight  of  the  flour  used  in 
making  it  ?  What  would  be  the  selling  price  for 
a  barrel  of  flour  at  5  s^^  a  loaf  for  the  bread  ? 

57.  The  average  workman  should  eat  daily  a 
certain  weight  of  starchy  food,  16  %  of  that  weight 
of  fats,  and  20  %  of  that  weight  of  albuminous  sub- 
stances. The  total  weight  of  these  three  food  sub- 
stances should  be  at  least  IJ  poimds  daily.  What 
weight  of  each  is  required  ? 

58.  About  11.2  %  of  an  egg  is  shell.  When 
eggs  are  35  i^  per  dozen,  what  is  spent  for  waste 
material  ? 


228  GENERAL  REVIEW 

59.  Cooked  eggs  contain  12%  protein  and 
cooked  roast  beef  22.3  %  protein.  If  one  egg 
weighs  2  ounces,  how  many  eggs  will  furnish  as 
much  protein  as  1  pound  of  roast  beef? 

60.  The  total  weight  of  an  egg  is  1.88  ounces. 
If  1.07  ounces  were  white,  .62  ounce  was  yolk,  and 
.19  ounce  was  water,  what  per  cent  of  each  made 
up  the  egg  ? 

61.  Milk  contains  about  87  %  water.  If  1  cup 
of  milk  weighs  8|  ounces,  how  many  pints  of  water 
are  found  in  a  gallon  of  milk  ? 

62.  Milk  contains  about  3  %  protein.  If  f  of 
the  protein  is  casein  and  J  albumen,  what  is  the 
per  cent  of  casein  and  albumen  in  milk  ? 

63.  Cooked  eggs  contain  13  %  protein.  What 
quantity  of  milk  contains  the  same  amount  of 
protein  as  one  dozen  eggs  ? 

64.  How  much  lace  is  needed  to  put  around  a 
dusting  cap  which  is  18  inches  in  diameter  ? 

65.  A  man  sold  two  engines  for  $2500  each. 
On  one  he  lost  25  %  and  on  the  other  he  gained 
25  %.  Did  he  gain  or  lose  on  the  entire  transac- 
tion and  how  much  ? 

66.  In  unskimmed  milk  .88  is  water,  .2  is  fat, 
.04  is  protein,  and  .05  is  carbohydrates.  How 
much  of  each  is  there  in  a  gallon  of  milk  ? 

67.  In  testing  wheat  for  seed  a  man  found  375 
good  seeds  out  of  every  425.     What  per  cent  of  the 


MISCELLANEOUS  PROBLEMS  229 

seeds  were  good  ?     If  he  paid  90  ^  per  bushel,  what 
was  the  price  paid  for  a  bushel  of  good  seed  ? 

68.  A  man  purchased  30  head  of  cattle  for  $1500 
and  kept  them  four  months.  During  that  time  he 
fed  them  an  average  of  |  ton  of  alfalfa  hay  per 
head  valued  at  $17  per  ton,  \  bushel  of  com  per 
day  per  head  at  75^  per  bushel,  and  100  tons  of 
silage  valued  at  $5  per  ton.  What  was  the  selling 
price  per  head  in  order  to  realize  a  gain  of  10  %  ? 

69.  A  farmer  offers  to  sell  a  horse  for  $180  cash, 
or  for  wheat  valued  at  $200.  What  will  he  re- 
ceive for  the  horse  if  he  is  paid  50  %  in  cash  and  the 
remainder  in  wheat  ?     Show  that  it  is  not  $190. 

70.  The  New  Hampshire  received  2250  tons  of 
coal  on  board  during  a  recent  coaling.  During  the 
next  two  weeks  1575  tons  of  it  were  burned. 
What  per  cent  of  the  coal  remained  ? 

71.  Water  in  freezing  expands  10  %  of  its  vol- 
ume. How  much  water  when  frozen  will  just  fill 
a  five-gallon  freezer  ? 

72.  At  the  Kansas  Experiment  Station  in  1912 
potatoes  raised  on  one  plot  which  was  plowed  in 
March  yielded  258  bushels  per  acre ;  when  plowed 
in  September  and  then  in  March,  the  yield  was 
then  287  bushels ;  when  plowed  in  July  and  then 
in  March,  339  bushels.  What  was  the  per  cent  of 
increase  of  each  yield  over  that  of  the  spring 
plowing  ? 


230  GENERAL  REVIEW 

73.  On  September  9,  1907,  1445  wheat  plants 
were  examined  for  Hessian  flies  and  119  plants 
were  infested.     What  per  cent  were  infested  ? 

74.  The  average  number  of  Hessian  flies  emerg- 
ing from  a  plot  of  untreated  ground  was  25.  By 
burning  the  trash  on  the  ground,  plowing,  disking, 
etc.,  only  an  average  of  one  fly  emerged.  What 
was  the  per  cent  of  gain  in  destruction  of  the  flies 
made  by  treating  the  ground  ? 

75.  If  alfalfa  hay  contains  10.58  %  protein, 
37.33  %  carbohydrates,  and  1.38%  fats;  and  timo- 
thy hay  contains  2.89  %  protein,  43.72  %  carbo- 
hydrates, and  1.43  %  fats,  what  is  the  difference 
in  the  feeding  value  of  a  ton  of  alfalfa  hay  and  a 
ton  of  timothy  hay,  estimating  protein  at  S^i^  a, 
pound,  carbohydrates  at  1  ^  a  pound,  and  fats  at 
2^^  a,  pound  ? 

76.  Which  is  cheaper,  a  ton  of  3:8:3  fertilizer 
at  $21,  or  a  ton  of  4  :  6  :  3  fertihzer  at  $24,  valuing 
nitrogen  at  18  J^,  phosphoric  acid  at  5^,  and  potash 
at  5  j^  per  pound  ? 

77.  A  cow  gives  during  a  certain  month  925 
pounds  of  milk  yielding  3.2  %  butter  fat.  If  the 
butter  fat  produces  f  of  its  weight  in  butter,  what 
is  the  value  of  the  butter  that  can  be  made  from 
it  at  25  ^  per  pound  ? 

78.  I  bought  a  6  %  $2500  mortgage  at  5  % 
discount,  with  two  years  to  run.     What  per  cent 


MISCELLANEOUS  PROBLEMS  231 

of  interest  is  realized  on  the  money  if  the  mortgage 
is  paid  at  maturity  ? 

79.  My  agent  sold  goods  to  the  amount  of 
$4620.  If  he  paid  $85  for  cartage  and  other  ex- 
penses, and  charged  3  %  commission,  what  were  the 
net  profits  ? 

80.  The  usual  charge  at  the  Chicago  stockyards 
for  selling  beef  cattle  is  50  '^  per  head.  Find  the 
per  cent  of  commission  on  35  head  of  cattle  weighs 
ing  1250  pounds  each  and  selling  for  $7.15  per 
hundredweight. 

81.  A  commission  merchant  sells  7000  pounds 
of  cotton  at  15^  per  pound,  charging  21%  com- 
mission. With  the  net  proceeds  he  buys  cotton 
cloth  at  VI '^  per  yard,  charging  2  %  commission 
for  buying.    How  many  yards  of  cloth  does  he  buy  ? 

82.  A  man's  house  was  damaged  by  a  wind  storm 
to  the  extent  of  30  %  of  its  value.  He  received 
from  the  insurance  company  in  which  the  house  was 
insured  for  80  %  of  its  value,  the  sum  of  $984,  cov- 
ering the  loss.     What  was  the  value  of  the  house  ? 

83.  If  under  like  field  conditions  one  variety  of 
wheat  yields  6  bushels  per  acre  more  than  another 
variety,  find  the  gain  in  planting  the  better  variety 
on  120  acres,  if  the  poor  seed  costs  65  i^  and  the 
better  seed  $1.45  per  bushel.  Allow  7  pecks  of 
seed  wheat  per  acre  and  reckon  the  value  of  the 
wheat  at  95  )2^  per  bushel. 


232  GENERAL  REVIEW 

84.  In  a  hog-fattening  experiment  it  was  found 
that  4.25  pounds  of  a  ration,  consisting  of  5  parts  of 
corn  meal  and  1  part  of  tankage,  produced  1  pound 
of  gain,  and  that  7.28  pounds  of  a  corn  meal  ration 
produced  1  pound  of  gain.  Determine  in  each 
case  the  cost  of  feed  per  100  pounds  of  gain ;  also 
find  the  amount  saved  per  100  pounds  of  gain  each 
for  15  hogs,  by  use  of  the  first  ration.  Value  corn 
meal  at  95^  per  hundredweight  and  tankage  at 
2^^  per  pound. 

85.  At  a  distance  of  60  feet  from  a  windmill  is 
a  post  10  feet  high.  By  standing  back  of  the  post 
6  feet  and  sighting  over  a  4-foot  stick  the  top  of 
the  windmill  and  the  top  of  the  post  are  in  line. 
How  high  is  the  windmill? 

86.  A  common  brick  weighs  4|^  pounds.  What 
is  its  specific  gravity  ? 

87.  A  cubic  foot  of  salt  water  weighs  64,375 
pounds.  What  does  a  column  of  water  weigh  that 
is  1  foot  square  and  60.5  feet  high  ? 

88.  The  specific  gravity  of  ice  is  .92.  What  is 
the  weight  of  a  block  of  ice  that  is  18  by  18  inches 
and  3  feet  long  ? 

89.  The  specific  gravity  of  machine  oil  is  .886. 
What  is  the  weight  of  a  barrel  of  oil  ? 

90.  Steel  expands  about  .00000636  of  an  inch 
for  every  inch  when  the  temperature  is  increased 
1  degree  F.     What  is  the  increase  in  length  of  a 


MISCELLANEOUS  PROBLEMS  233 

rail  for  a  railroad,  if  the  rail  is  60  feet  long  and  the 
temperature  rises  5  degrees  ?  What  would  be  the 
increase  in  length  if  there  were  a  change  from  a 
winter  temperature  of  8  degrees  below  zero  to  a 
summer  heat  of  90  degrees? 

91.  What  is  the  weight  of  a  cubic  inch  of  gold 
if  its  specific  gravity  is  19.245  ?  Of  mercury,  spe- 
cific gravity  of  13.587  ?  Of  lead,  specific  gravity  of 
11.07? 

92.  A  dairy  cow  requires  1  pound  of  protein  to 
6  pounds  of  carbohydrates  in  her  food.  Dry  peas 
contain  10  pounds  protein  and  32  pounds  carbohy- 
drates per  bushel  (60  lb.).  Hay  contains  88 
pounds  of  protein  and  880  pounds  of  carbohydrates 
per  ton.  What  should  be  the  proportion  of  the 
quantities  of  dry  peas  and  hay  fed  to  a  dairy  cow, 
if  these  are  to  constitute  her  feed  ? 

93.  How  many  gallons  each  of  cream  containing 
30  %  fat  and  milk  containing  5  %  fat,  can  be 
mixed  so  as  to  produce  10  gallons  of  cream  con- 
taining 25  %  fat  ? 

94.  A  65-foot  ladder  rests  against  a  building,  its 
foot  being  39  feet  from  the  wall.  How  high  does 
it  reach  ? 

95.  Three  men  owning  lots  with  frontages  of 
40,  55,  and  65  feet  respectively  on  the  same  street 
are  assessed  $475  for  curbing  and  paving.  Find 
the  share  of  each. 


234  GENERAL  REVIEW 

96.  If  a  water  pipe  can  fill  a  cistern  holding  90 
barrels  in  32  minutes  30  seconds,  how  long  will  it 
take  for  the  same  pipe  to  fill  a  cistern  holding  145 
barrels  ? 

97.  Find  to  two  decimal  places  the  diagonal  of  a 
square  field  containing  17  acres  110  sq.  rd. 

98.  A  cotton  planter  mixed  a  ton  of  fertilizer 
for  his  land,  containing  85  parts  of  acid  phosphate, 
105  parts  of  cotton  seed  meal,  and  10  parts  of  muri- 
ate of  potash.  What  was  the  cost  of  the  fertilizer 
if  the  prices  of  the  ingredients  were  $10.75, 
$25.40,  and  $41.25  per  ton  respectively  ? 

99.  A  1916  bulletin  issued  by  the  United  States 
Department  of  Agriculture  on  the  Cost  of  Fencing 
in  the  Central  States  shows  that  there  are  6,361,502 
farms  in  the  United  States  averaging  138.1  acres 
and  requiring  on  the  average  6  rods  of  fence  per 
acre.  What  is  the  total  number  of  rods  of  fence  ? 
The  total  number  of  miles  ?  How  many  times 
would  this  number  of  miles  of  fence  encircle  the 
earth  ? 

100.  To  replace  this  with  a  medium  grade  of 
woven  wire  fence  would  cost  65^  a  rod.  What 
would  be  the  total  cost  of  the  fence  in  problem  99  ? 

101.  The  cost  of  the  fence  in  problem  100  is 
8.3  %  of  the  value  of  the  farm  property  and  12  % 
of  the  value  of  the  farm  land  in  the  United  States. 
What  is  the  value  of  each  ? 


APPENDIX   I 

•    WEIGHTS   OF  PRODUCE 

I.    The  following  are  the  weights  per  bushel  of  certain 
articles  according  to  the  laws  of  the  various  states : 

Wheat 60  lb.  in  all  states. 

Ear  corn  .....     70  lb.  in  all  except  Ohio  68  lb. ;  in 

Indiana  after  Dec.  1,  and  in 
Kentucky  after  May  1,  68  lb. 

Shelled  corn      ...     56  lb.  except  California  52  lb. 

Oats 32  lb.  except  Idaho  36  lb. ;  Maryland 

26  lb. ;  Virginia  and  New  Jersey 
30  lb. 

Rye 56  lb.  except  California  54  lb. ;  Maine 

50  lb. 

Barley 48  lb.  except  Oregon  46  lb. ;  Califor- 
nia 50  lb. ;  Alabama,  Georgia, 
Kentucky,  Pennsylvania  47  lb. 

Beans 60  lb.  in  all  states. 

Peas 60  lb.  in  all  states. 

Potatoes 60  lb.  except  Maryland,  Pennsyl- 
vania, and  Virginia  56  lb. 

Sweet  potatoes       .     .     55  lb.  in  most  states,  50  lb.  in  Kansas. 

Onions 57  lb.  in  nearly  all  states. 

Turnips 55  lb.  in  all  states. 

Clover  seed  .     .     .     .     60  lb.  except  Kew  Jersey  64  lb. 

Alfalfa 60  lb.  except  ISTew  Jersey  64  lb. 

Timothy  seed    ...     45  lb.  except  Arkansas  60  lb. ;  North 

Dakota  and  Oklahoma  42  lb. 
236 


236  APPENDIX  I 

Hungarian  grass  seed     50  lb.  in  all  states. 

Millet 50  lb.  in  all  states. 

Flax  seed      .     .     .     .     56  lb.  in  all  states. 

Blue-grass  seed      .     .     14  lb.  in  all  states. 

Coal 80  lb.  in  all  states. 

Apples 48  lb.  except  Arkansas,  Minnesota, 

New  Jersey,  North  Dakota, 
Ohio,  Tennessee,  and  Wiscon- 
sin 50  lb. ;  Idaho,  Montana,  Ore- 
gon, Texas,  and  Washington 
45  lb. ;  Maine  44  lb. 

Bran 20  lb.  in  all  states. 

IMPORTANT   FACTS 

II.  1  cubic  foot  of  water  weighs  62^  pounds  or  1000 
oxinces. 

1  gallon  of  water  weighs  8^  pounds. 

1  cubic  foot  of  water  equals  7^  gallons. 

1  cubic  foot  equals  f  of  a  bushel. 

1  pound  avoirdupois  equals  7000  grains. 

1  pound  Troy  equals  5760  grains. 

1  barrel  equals  31  i-  gallons  or  4.211  cubic  feet. 

196  pounds  of  flour  equals  one  barrel. 

200  pounds  of  pork  or  beef  equals  one  barrel. 

SPECIAL  RULES 

III.  The  surface  of  a  pyramid  or  cone  equals  one  half 
the  perimeter  of  the  base  times  the  slant  height. 

The  volume  of  a  pyramid  or  cone  equals  one  third  the 
area  of  the  base  times  the  height. 

The  surface  of  the  frustum  of  a  pyramid  or  cone  equals 
one  half  the  slant  height  times  the  sum  of  the  perimeters 
of  the  two  bases. 


APPENDIX  I  237 

The  volume  of  the  frustum  of  a  pyramid  or  cone  equals 
^  the  height  times  the  sum  of  the  two  bases  plus  the  square 
root  of  their  product. 

The  surface  of  a  sphere  equals  4  7r  times  the  square  of 
the  radius. 

The  volume  of  a  sphere  equals  f  tt  times  the  radius  cubed. 

HAY   MEASUREMENTS 

IV.  To  measure  hay  in  the  mow,  multiply  the  length, 
width,  and  depth  in  feet  together  and  divide  by  405,  if  the 
hay  is  well  settled  and  the  mow  deep.  If  the  mow  is  shal- 
low and  recently  filled  allow  512  cubic  feet  to  the  ton. 

Alfalfa  hay  that  has  been  stacked  30  days  will  require 
about  512  cubic  feet  for  a  ton.  When  the  hay  has  been 
stacked  5  or  6  months,  usually  422  cubic  feet  is  calculated 
for  a  ton.  In  old  fully  settled  stacks,  about  350  cubic  feet 
will  be  about  right. 

To  find  the  number  of  tons  in  a  rick,  measure  the  distance 
in  feet  from  the  bottom  of  the  rick  on  one  side  to  the  bottom 
on  the  other ;  add  to  this  the  average  width  of  the  rick  in 
feet,  divide  this  sum  by  4  and  multiply  the  quotient  by 
itself  and  this  product  by  the  length  of  the  rick  in  feet. 
This  will  give  the  number  of  cubic  feet  in  the  rick.  Divide 
by  512,  422,  or  350  to  find  the  number  of  tons. 

For  a  conical  stack :  find  the  circumference  at  or  above 
the  base  or  bulge  at  a  height  that  will  average  the  base  from 
there  to  the  ground ;  find  the  vertical  height  of  the  meas- 
ured circumference  from  the  ground  and  the  slant  height 
from  the  measured  circumference  to  the  top  of  the  stack  in 
feet.  Multiply  the  circumference  by  itself ;  divide  by  100 ; 
and  multiply  by  8 ;  then  multiply  the  result  by  the  height 
of  the  base  plus  one  third  of  the  slant  height  of  the  top. 
Divide  by  512,  422,  or  350  to  find  the  number  of  tons. 


APPENDIX   II 

MISCELLANEOUS  MEASURES 
V.     Tables  for  Reference 


Use   this 

Special    Linear    Units    Table    for 

Reference 

1  hand 

=  4  inches.  Used  in  measuring  the 
height  of  a  horse. 

1  fathom 

=  6  feet.  Used  in  measuring  depths 
at  sea. 

1  knot  (geog.  mile) 

=  1.152|  miles  or  6086  ft.     Used  for 

measuring  distances  at  sea. 

Paper 


Table 

FOR  Reference 

24  sheets 

=  1  quire 

20  quires 

=  1  ream 

2  reams 

=  1  bimdle 

5  bundles 

=  1  bale 

This  table  for  counting  sheets  of  paper  was  for- 
merly used  extensively  in  the  printing  and  publish- 
ing business.  Paper  is  now  usually  counted  in 
bundles  of  500  sheets. 

238 


APPENDIX  II  239 

Counting 


Use 

THE  Table  in  Counting 

12 

things 

=  1  dozen  (doz.) 

20 

things 

=  1  score 

12  dozen 

=  1  gross 

12 

gross 

=  1  great  gross 

Circular  Measure 


Circular  Measure  is  used  in  measuring  angles  or 
arcs  of  circles.  The  unit  is  the  degree  which  is  3-^^ 
of  the  circumference  of  a  circle.  At  the  equator  1 
degree  equals  Q9^  miles,  or  60  knots. 


Table  for  Eeference 

60  seconds(")  =  1  minute  (') 
60  minutes      =  1  degree  (°) 
360  degrees       =  1  circumference 


Troy  Weight 

Troy  Weight  is  used  in  weighing  diamonds,  gold, 
silver,  and  other  precious  metals. 


Table  for  Keference 

24  grains  (gr.)     =  1  pennyweight  (pwt.) 
20  pennyweight  =  1  ounce 
12  ounces  =  1  pound 


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Community  Civics  is  a  moving  treatment  of  civic  affairs  in  the  com- 
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